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**## Topic2Assignment-BUS-660-O500_071725_091025_ZwanzigerElsingerSummer22025_WebAssign.pdf**
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csmall13@my.gcu.edu Sign out
BUS-660-O500_071725_091025_ZwanzigerElsinger, Summer 2 2025
Topic 2 Assignment (Homework)
INSTRUCTOR
Summer Zwanziger Elsinger
Grand Canyon University, AZ
Home My Assignments
Grades Communication
Calendar
Current Score: 2 / 84 POINTS | 2.4 %
Scoring and Assignment Information
Due Date: THU, JUL 31, 2025 4:00 AM CDT REQUEST EXTENSION
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CammIMS16 4.E.001.
A linear programming computer package is needed.
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs.
Currently, promotional plans are under way for this year's program. Advertising alternatives include
television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as
shown.
Constraint Television Radio Online
Audience per advertisement 400,000 72,000 160,000
Cost per advertisement $2,000 $300 $600
Maximum media usage 10 20 10
To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total
number of advertisements authorized. In addition, television should account for at least 10% of the total
number of advertisements authorized.
(a) If the promotional budget is limited to $22,800, how many commercial messages should be run on
each medium to maximize total audience contact?
Television 6
Radio 3
Online 10
What is the allocation of the budget among the three media, and what is the total audience reached?
Television Budget 12,000
Radio Budget 900
Online Budget 6000
Total Audience 3936000
(b) By how much would audience contact increase if an extra $100 were allocated to the promotional
budget? (Round your answer to the nearest whole number.)
267
1. [2 / 8 Points]
DETAILS MY NOTES PREVIOUS ANSWERS ASK YOUR TEACHER
PRACTICE ANOTHER
CammIMS16 4.E.003.
A linear programming computer package is needed.
The employee credit union at State University is planning the allocation of funds for the coming year. The
credit union makes four types of loans to its members. In addition, the credit union invests in risk-free
securities to stabilize income. The various revenue-producing investments together with annual rates of
return are as follows.
Type of Loan/Investment Annual Rate of Return (%)
Automobile loans 9
Furniture loans 11
Other secured loans 12
Signature loans 13
Risk-free securities 10
The credit union will have $2,200,000 available for investment during the coming year. State laws and
credit union policies impose the following restrictions on the composition of the loans and investments.
Risk-free securities may not exceed 30% of the total funds available for investment.
Signature loans may not exceed 10% of the funds invested in all loans (automobile,
furniture, other secured, and signature loans).
Furniture loans plus other secured loans may not exceed the automobile loans.
Other secured loans plus signature loans may not exceed the funds invested in risk-free
securities.
How should the $2,200,000 be allocated to each of the loan/investment alternatives to maximize total
annual return?
Automobile loans $ 660000
Furniture loans $ 220000
Other secured loans $ 440000
Signature loans $ 220,000
Risk-free securities $ 660,000
What is the projected total annual return?
2. [0 / 6 Points]
DETAILS MY NOTES PREVIOUS ANSWERS ASK YOUR TEACHER
PRACTICE ANOTHER
$ 231,000
CammIMS16 4.E.005.
A linear programming computer package is needed.
Kilgore's Deli is a small delicatessen located near a major university. Kilgore does a large walk-in carry-out
lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day,
Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The
profit on one serving of Wimpy is $0.44, on one serving of Dial 911, $0.57. Each serving of Wimpy requires
0.25 pound of beef, 0.25 cup of onions, and 5 ounces of Kilgore's special sauce. Each serving of Dial 911
requires 0.25 pound of beef, 0.4 cup of onions, 2 ounces of Kilgore's special sauce, and 5 ounces of hot
sauce. Today, Kilgore has 18 pounds of beef, 13 cups of onions, 86 ounces of Kilgore's special sauce, and 58
ounces of hot sauce on hand.
(a) Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911
to make in order to maximize his profit today. (Let W = the number of servings of Wimpy to make
and let D = the number of servings of Dial 911 to make.)
Max
s.t.
Beef
Onions
Special Sauce
Hot Sauce
(b) Find an optimal solution. (Round your answers to two decimal places.)
3. [– / 14 Points]
DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
W, D ≥ 0
Profit = $
(c) What is the dual value for special sauce? (Round your answer to two decimal places.)
$
Interpret the dual value.
For every 1 ounce increase in —Select— , the profit will —Select— by $ .
(d) Increase the amount of special sauce available by 1 ounce and re-solve. (Round your answers to two
decimal places.)
Profit = $
Does the solution confirm the answer to part (c)?
Yes
No
(W, D) =
(W, D) =
CammIMS16 4.E.007.
A linear programming computer package is needed.
As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to
make the following annual payments (in thousands of dollars).
Year 1 2 3 4 5 6
Payment 200 225 250 295 325 470
The annual payments must be made at the beginning of each year. The judge will approve an amount that,
along with earnings on its investment, will cover the annual payments. Investment of the funds will be
limited to savings (at 4% annually) and government securities, at prices and rates currently quoted in The
Wall Street Journal.
Hoxworth wants to develop a plan for making the annual payments by investing in the following securities
(par value = $1,000). Funds not invested in these securities will be placed in savings.
Security Current Price Rate (%) Years to Maturity
1 $1,055 6.750 3
2 $1,000 5.125 4
Assume that interest is paid annually. The plan will be submitted to the judge and, if approved, Hoxworth
will be required to pay a trustee the amount that will be required to fund the plan.
(a) Use linear programming to find the minimum cash settlement necessary (in $) to fund the annual
payments. (Round your answer to the nearest dollar.)
$
(b) Use the dual value to determine how much more (in $) Hoxworth should be willing to pay now to
reduce the payment at the beginning of year 6 to $400,000. (Round your answer to the nearest
dollar.)
$
(c) Use the dual value to determine how much more (in $) Hoxworth should be willing to pay to reduce
the year 1 payment to $150,000. (Round your answer to the nearest dollar.)
$
(d) Suppose that the annual payments are to be made at the end of each year. Reformulate the model to
accommodate this change. How much would Hoxworth save (in $) if this change could be negotiated?
4. [– / 4 Points]
DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
(Round your answer to the nearest dollar.)
$
CammIMS16 4.E.009.
A linear programming computer package is needed.
Epsilon Airlines services predominately the eastern and southeastern United States. A vast majority of
Epsilon's customers make reservations through Epsilon's website, but a small percentage of customers
make reservations via phone. Epsilon employs call-center personnel to handle these reservations along with
any problems with the website reservation system and for the rebooking of flights for customers if their
plans change or their travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon's
management team. Having too many employees on hand is a waste of money, but having too few results in
very poor customer service and the potential loss of customers.
Epsilon analysts have estimated the minimum number of call-center employees needed by day of week for
the upcoming vacation season (June, July, and the first two weeks of August). These estimates are given in
the following table.
Day
Minimum Number of
Employees Needed
Monday 85
Tuesday 60
Wednesday 55
Thursday 75
Friday 105
Saturday 85
Sunday 55
The call-center employees work five consecutive days and then have two consecutive days off. An employee
may start work any day of the week. Each call-center employee receives the same salary. Assume that the
schedule cycles and ignore start-up and stopping of the schedule. Develop a model that will minimize the
total number of call-center employees needed to meet the minimum requirements. (Let = the number of
call-center employees who start work on day i where etc).
Min
5. [– / 10 Points]
DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
Xi
i = 1 = Monday, i = 2 = Tuesday,
s.t.
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Find the optimal solution.
X , X , X , X , X , X , X ≥ 01 2 3 4 5 6 7
Give the number of call-center employees that exceed the minimum required.
(X , X , X , X , X , X , X ) =
1 2 3 4 5 6 7
(M, Tu, W, Th, F, Sa, Su) =
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javascript:open_bc_enhanced('watch_it', 'https://wowzahttp.cengage.com/nextbook/decision_sciences/camm_675626/student/video/04_09/04_09_hi.mp4', 1)
CammIMS16 4.E.011.
A linear programming computer package is needed.
Edwards Manufacturing Company purchases two component parts from three different suppliers. The
suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the
suppliers charge different prices for the components. Component price data (in price per unit) are as
follows.
Component
Supplier
1 2 3
1 $13 $14 $15
2 $11 $12 $11
Each supplier has a limited capacity in terms of the total number of components it can supply. However, as
long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1,
component 2, or any combination of the two components, if the total number of units ordered is within its
capacity. Supplier capacities are as follows.
Supplier 1 2 3
Capacity 700 1,100 900
(a) If the Edwards production plan for the next period includes 1,100 units of component 1 and 900 units
of component 2, what purchases do you recommend? That is, how many units of each component
should be ordered from each supplier?
Component 1, Supplier 1 units
Component 1, Supplier 2 units
Component 1, Supplier 3 units
Component 2, Supplier 1 units
Component 2, Supplier 2 units
Component 2, Supplier 3 units
(b) What is the total purchase cost (in $) for the components?
$
6. [– / 7 Points]
DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
CammIMS16 4.E.017.
A linear programming computer package is needed.
Frandec Company manufactures, assembles, and rebuilds material-handling equipment used in warehouses
and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a
motor, two supports, and a metal strap. Frandec's production schedule calls for 4,500 Liftmasters to be
made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and
straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing
and purchase costs per unit are shown.
Component Manufacturing Cost Purchase Cost
Frame $39.00 $52.00
Support $12.50 $16.00
Strap $7.50 $8.50
Three departments are involved in the production of these components. The time (in minutes per unit)
required to process each component in each department and the available capacity (in hours) for the three
departments are as follows.
Component
Department
Cutting Milling Shaping
Frame 3.5 2.2 3.1
Support 1.3 1.7 2.6
Strap 0.8 — 1.7
Capacity (hours) 350 420 680
(a) Formulate and solve a linear programming model for this make-or-buy application. (Let FM = number
of frames manufactured, FP = number of frames purchased, SM = number of supports manufactured,
SP = number of supports purchased, TM = number of straps manufactured, and TP = number of
straps purchased. Express time in minutes per unit.)
Min
7. [– / 16 Points]
DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
Cutting constraint
Milling constraint
Shaping constraint
Frame constraint
Support constraint
Strap constraint
How many of each component should be manufactured and how many should be purchased? (Round
your answers to the nearest whole number.)
(FM, FP, SM, SP, TM, TP) =
(b) What is the total cost (in $) of the manufacturing and purchasing plan?
$
FM, FP, SM, SP, TM, TP ≥ 0
(c) How many hours of production time are used in each department? (Round your answers to two
decimal places.)
Cutting hrs
Milling hrs
Shaping hrs
(d) How much (in $) should Frandec be willing to pay for an additional hour of time in the shaping
department?
$
(e) Another manufacturer has offered to sell frames to Frandec for $45 each. Could Frandec improve its
position by pursuing this opportunity? Why or why not? (Round your answer to three decimal places.)
—Select— . From the results of the model in part (a), the variable FP has a reduced cost of
, which indicates that the solution —Select— be improved if the purchase cost of
frames can be lowered to $45 each.
CammIMS16 5.E.007.
A linear programming computer package is needed.
Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When
a convention or a special event is in town, Hanson increases its normal room rates and takes reservations
based on a revenue management system. A large profesional organization has scheduled its annual
convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its rooms
available for convention attendees at a special convention rate in order to be listed as a recommended hotel
for the convention. Although the majority of attendees at the annual meeting typically request a Friday and
Saturday two-night package, some attendees may select a Friday night only or a Saturday night only
reservation. Customers not attending the convention may also request a Friday and Saturday two-night
package, or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are
possible: Convention customers/two-night package; convention customers/Friday night only; convention
customers/Saturday night only; regular customers/two-night package; regular customers/Friday night only;
and regular customers/Saturday night only. The cost for each type of reservation is shown below.
Two-Night
Package
Friday Night
Only
Saturday Night
Only
Convention $225 $123 $130
Regular $295 $146 $152
The anticipated demand for each type of reservation is as follows.
Two-Night
Package
Friday Night
Only
Saturday Night
Only
Convention 40 20 15
Regular 20 30 25
Hanson Inn would like to determine how many rooms to make available for each type of reservation in
order to maximize total revenue.
(a) Formulate a linear programming model for this revenue management application. (Let CT = number
of convention two-night rooms, CF = number of convention Friday only rooms, CS = number of
convention Saturday only rooms, RT = number of regular two-night rooms, RF = number of regular
Friday only rooms, RS = number of regular Saturday only rooms.)
Max
8. [– / 19 Points] DETAILS MY NOTES ASK YOUR TEACHER
s.t.
anticipated demand for convention two-night rooms
anticipated demand for convention Friday night only rooms
anticipated demand for convention Saturday night only rooms
anticipated demand for regular two-night rooms
anticipated demand for regular Friday night only rooms
anticipated demand for regular Saturday night only rooms
Friday night rooms available for convention attendees only
Saturday night rooms available for convention attendees only
total rooms available for Friday night
total rooms available for Saturday night
(b) What is the optimal allocation?
CT =
CF =
CS =
RT =
RF =
RS =
From this allocation, what is the anticipated total revenue (in dollars)?
$
(c) Suppose that one week before the convention the number of regular customers/Saturday night only
rooms that were made available sell out. If another nonconvention customer calls and requests a
Saturday night only room, what is the value (in dollars) of accepting this additional reservation?
If the hotel accepts this additional reservation, then the total profit would increase by
$ .
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CT, CF, CS, RT, RF, RS ≥ 0
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**## Topic2Assignment-BUS-660-O500_071725_091025_ZwanzigerElsingerSummer22025_WebAssign.pdf**
EN
csmall13@my.gcu.edu Sign out
BUS-660-O500_071725_091025_ZwanzigerElsinger, Summer 2 2025
Topic 2 Assignment (Homework)
INSTRUCTOR
Summer Zwanziger Elsinger
Grand Canyon University, AZ
Home My Assignments
Grades Communication
Calendar
Current Score: 2 / 84 POINTS | 2.4 %
Scoring and Assignment Information
Due Date: THU, JUL 31, 2025 4:00 AM CDT REQUEST EXTENSION
[https://www.cengage.com/dashboard/](https://www.cengage.com/dashboard/)
[https://www.webassign.net/manual/student_guide/](https://www.webassign.net/manual/student_guide/)
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CammIMS16 4.E.001.
A linear programming computer package is needed.
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs.
Currently, promotional plans are under way for this year's program. Advertising alternatives include
television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as
shown.
Constraint Television Radio Online
Audience per advertisement 400,000 72,000 160,000
Cost per advertisement $2,000 $300 $600
Maximum media usage 10 20 10
To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total
number of advertisements authorized. In addition, television should account for at least 10% of the total
number of advertisements authorized.
(a) If the promotional budget is limited to $22,800, how many commercial messages should be run on
each medium to maximize total audience contact?
Television 6
Radio 3
Online 10
What is the allocation of the budget among the three media, and what is the total audience reached?
Television Budget 12,000
Radio Budget 900
Online Budget 6000
Total Audience 3936000
(b) By how much would audience contact increase if an extra $100 were allocated to the promotional
budget? (Round your answer to the nearest whole number.)
267
1. [2 / 8 Points]
DETAILS MY NOTES PREVIOUS ANSWERS ASK YOUR TEACHER
PRACTICE ANOTHER
CammIMS16 4.E.003.
A linear programming computer package is needed.
The employee credit union at State University is planning the allocation of funds for the coming year. The
credit union makes four types of loans to its members. In addition, the credit union invests in risk-free
securities to stabilize income. The various revenue-producing investments together with annual rates of
return are as follows.
Type of Loan/Investment Annual Rate of Return (%)
Automobile loans 9
Furniture loans 11
Other secured loans 12
Signature loans 13
Risk-free securities 10
The credit union will have $2,200,000 available for investment during the coming year. State laws and
credit union policies impose the following restrictions on the composition of the loans and investments.
Risk-free securities may not exceed 30% of the total funds available for investment.
Signature loans may not exceed 10% of the funds invested in all loans (automobile,
furniture, other secured, and signature loans).
Furniture loans plus other secured loans may not exceed the automobile loans.
Other secured loans plus signature loans may not exceed the funds invested in risk-free
securities.
How should the $2,200,000 be allocated to each of the loan/investment alternatives to maximize total
annual return?
Automobile loans $ 660000
Furniture loans $ 220000
Other secured loans $ 440000
Signature loans $ 220,000
Risk-free securities $ 660,000
What is the projected total annual return?
2. [0 / 6 Points]
DETAILS MY NOTES PREVIOUS ANSWERS ASK YOUR TEACHER
PRACTICE ANOTHER
$ 231,000
CammIMS16 4.E.005.
A linear programming computer package is needed.
Kilgore's Deli is a small delicatessen located near a major university. Kilgore does a large walk-in carry-out
lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day,
Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The
profit on one serving of Wimpy is $0.44, on one serving of Dial 911, $0.57. Each serving of Wimpy requires
0.25 pound of beef, 0.25 cup of onions, and 5 ounces of Kilgore's special sauce. Each serving of Dial 911
requires 0.25 pound of beef, 0.4 cup of onions, 2 ounces of Kilgore's special sauce, and 5 ounces of hot
sauce. Today, Kilgore has 18 pounds of beef, 13 cups of onions, 86 ounces of Kilgore's special sauce, and 58
ounces of hot sauce on hand.
(a) Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911
to make in order to maximize his profit today. (Let W = the number of servings of Wimpy to make
and let D = the number of servings of Dial 911 to make.)
Max
s.t.
Beef
Onions
Special Sauce
Hot Sauce
(b) Find an optimal solution. (Round your answers to two decimal places.)
3. [– / 14 Points]
DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
W, D ≥ 0
Profit = $
(c) What is the dual value for special sauce? (Round your answer to two decimal places.)
$
Interpret the dual value.
For every 1 ounce increase in —Select— , the profit will —Select— by $ .
(d) Increase the amount of special sauce available by 1 ounce and re-solve. (Round your answers to two
decimal places.)
Profit = $
Does the solution confirm the answer to part (c)?
Yes
No
(W, D) =
(W, D) =
CammIMS16 4.E.007.
A linear programming computer package is needed.
As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to
make the following annual payments (in thousands of dollars).
Year 1 2 3 4 5 6
Payment 200 225 250 295 325 470
The annual payments must be made at the beginning of each year. The judge will approve an amount that,
along with earnings on its investment, will cover the annual payments. Investment of the funds will be
limited to savings (at 4% annually) and government securities, at prices and rates currently quoted in The
Wall Street Journal.
Hoxworth wants to develop a plan for making the annual payments by investing in the following securities
(par value = $1,000). Funds not invested in these securities will be placed in savings.
Security Current Price Rate (%) Years to Maturity
1 $1,055 6.750 3
2 $1,000 5.125 4
Assume that interest is paid annually. The plan will be submitted to the judge and, if approved, Hoxworth
will be required to pay a trustee the amount that will be required to fund the plan.
(a) Use linear programming to find the minimum cash settlement necessary (in $) to fund the annual
payments. (Round your answer to the nearest dollar.)
$
(b) Use the dual value to determine how much more (in $) Hoxworth should be willing to pay now to
reduce the payment at the beginning of year 6 to $400,000. (Round your answer to the nearest
dollar.)
$
(c) Use the dual value to determine how much more (in $) Hoxworth should be willing to pay to reduce
the year 1 payment to $150,000. (Round your answer to the nearest dollar.)
$
(d) Suppose that the annual payments are to be made at the end of each year. Reformulate the model to
accommodate this change. How much would Hoxworth save (in $) if this change could be negotiated?
4. [– / 4 Points]
DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
(Round your answer to the nearest dollar.)
$
CammIMS16 4.E.009.
A linear programming computer package is needed.
Epsilon Airlines services predominately the eastern and southeastern United States. A vast majority of
Epsilon's customers make reservations through Epsilon's website, but a small percentage of customers
make reservations via phone. Epsilon employs call-center personnel to handle these reservations along with
any problems with the website reservation system and for the rebooking of flights for customers if their
plans change or their travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon's
management team. Having too many employees on hand is a waste of money, but having too few results in
very poor customer service and the potential loss of customers.
Epsilon analysts have estimated the minimum number of call-center employees needed by day of week for
the upcoming vacation season (June, July, and the first two weeks of August). These estimates are given in
the following table.
Day
Minimum Number of
Employees Needed
Monday 85
Tuesday 60
Wednesday 55
Thursday 75
Friday 105
Saturday 85
Sunday 55
The call-center employees work five consecutive days and then have two consecutive days off. An employee
may start work any day of the week. Each call-center employee receives the same salary. Assume that the
schedule cycles and ignore start-up and stopping of the schedule. Develop a model that will minimize the
total number of call-center employees needed to meet the minimum requirements. (Let = the number of
call-center employees who start work on day i where etc).
Min
5. [– / 10 Points]
DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
Xi
i = 1 = Monday, i = 2 = Tuesday,
s.t.
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Find the optimal solution.
X , X , X , X , X , X , X ≥ 01 2 3 4 5 6 7
Give the number of call-center employees that exceed the minimum required.
(X , X , X , X , X , X , X ) =
1 2 3 4 5 6 7
(M, Tu, W, Th, F, Sa, Su) =
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CammIMS16 4.E.011.
A linear programming computer package is needed.
Edwards Manufacturing Company purchases two component parts from three different suppliers. The
suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the
suppliers charge different prices for the components. Component price data (in price per unit) are as
follows.
Component
Supplier
1 2 3
1 $13 $14 $15
2 $11 $12 $11
Each supplier has a limited capacity in terms of the total number of components it can supply. However, as
long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1,
component 2, or any combination of the two components, if the total number of units ordered is within its
capacity. Supplier capacities are as follows.
Supplier 1 2 3
Capacity 700 1,100 900
(a) If the Edwards production plan for the next period includes 1,100 units of component 1 and 900 units
of component 2, what purchases do you recommend? That is, how many units of each component
should be ordered from each supplier?
Component 1, Supplier 1 units
Component 1, Supplier 2 units
Component 1, Supplier 3 units
Component 2, Supplier 1 units
Component 2, Supplier 2 units
Component 2, Supplier 3 units
(b) What is the total purchase cost (in $) for the components?
$
6. [– / 7 Points]
DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
CammIMS16 4.E.017.
A linear programming computer package is needed.
Frandec Company manufactures, assembles, and rebuilds material-handling equipment used in warehouses
and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a
motor, two supports, and a metal strap. Frandec's production schedule calls for 4,500 Liftmasters to be
made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and
straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing
and purchase costs per unit are shown.
Component Manufacturing Cost Purchase Cost
Frame $39.00 $52.00
Support $12.50 $16.00
Strap $7.50 $8.50
Three departments are involved in the production of these components. The time (in minutes per unit)
required to process each component in each department and the available capacity (in hours) for the three
departments are as follows.
Component
Department
Cutting Milling Shaping
Frame 3.5 2.2 3.1
Support 1.3 1.7 2.6
Strap 0.8 — 1.7
Capacity (hours) 350 420 680
(a) Formulate and solve a linear programming model for this make-or-buy application. (Let FM = number
of frames manufactured, FP = number of frames purchased, SM = number of supports manufactured,
SP = number of supports purchased, TM = number of straps manufactured, and TP = number of
straps purchased. Express time in minutes per unit.)
Min
7. [– / 16 Points]
DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER
Cutting constraint
Milling constraint
Shaping constraint
Frame constraint
Support constraint
Strap constraint
How many of each component should be manufactured and how many should be purchased? (Round
your answers to the nearest whole number.)
(FM, FP, SM, SP, TM, TP) =
(b) What is the total cost (in $) of the manufacturing and purchasing plan?
$
FM, FP, SM, SP, TM, TP ≥ 0
(c) How many hours of production time are used in each department? (Round your answers to two
decimal places.)
Cutting hrs
Milling hrs
Shaping hrs
(d) How much (in $) should Frandec be willing to pay for an additional hour of time in the shaping
department?
$
(e) Another manufacturer has offered to sell frames to Frandec for $45 each. Could Frandec improve its
position by pursuing this opportunity? Why or why not? (Round your answer to three decimal places.)
—Select— . From the results of the model in part (a), the variable FP has a reduced cost of
, which indicates that the solution —Select— be improved if the purchase cost of
frames can be lowered to $45 each.
CammIMS16 5.E.007.
A linear programming computer package is needed.
Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When
a convention or a special event is in town, Hanson increases its normal room rates and takes reservations
based on a revenue management system. A large profesional organization has scheduled its annual
convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its rooms
available for convention attendees at a special convention rate in order to be listed as a recommended hotel
for the convention. Although the majority of attendees at the annual meeting typically request a Friday and
Saturday two-night package, some attendees may select a Friday night only or a Saturday night only
reservation. Customers not attending the convention may also request a Friday and Saturday two-night
package, or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are
possible: Convention customers/two-night package; convention customers/Friday night only; convention
customers/Saturday night only; regular customers/two-night package; regular customers/Friday night only;
and regular customers/Saturday night only. The cost for each type of reservation is shown below.
Two-Night
Package
Friday Night
Only
Saturday Night
Only
Convention $225 $123 $130
Regular $295 $146 $152
The anticipated demand for each type of reservation is as follows.
Two-Night
Package
Friday Night
Only
Saturday Night
Only
Convention 40 20 15
Regular 20 30 25
Hanson Inn would like to determine how many rooms to make available for each type of reservation in
order to maximize total revenue.
(a) Formulate a linear programming model for this revenue management application. (Let CT = number
of convention two-night rooms, CF = number of convention Friday only rooms, CS = number of
convention Saturday only rooms, RT = number of regular two-night rooms, RF = number of regular
Friday only rooms, RS = number of regular Saturday only rooms.)
Max
8. [– / 19 Points] DETAILS MY NOTES ASK YOUR TEACHER
s.t.
anticipated demand for convention two-night rooms
anticipated demand for convention Friday night only rooms
anticipated demand for convention Saturday night only rooms
anticipated demand for regular two-night rooms
anticipated demand for regular Friday night only rooms
anticipated demand for regular Saturday night only rooms
Friday night rooms available for convention attendees only
Saturday night rooms available for convention attendees only
total rooms available for Friday night
total rooms available for Saturday night
(b) What is the optimal allocation?
CT =
CF =
CS =
RT =
RF =
RS =
From this allocation, what is the anticipated total revenue (in dollars)?
$
(c) Suppose that one week before the convention the number of regular customers/Saturday night only
rooms that were made available sell out. If another nonconvention customer calls and requests a
Saturday night only room, what is the value (in dollars) of accepting this additional reservation?
If the hotel accepts this additional reservation, then the total profit would increase by
$ .
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