A linear programming computer package is needed

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BUS-660-O500_071725_091025_ZwanzigerElsinger, Summer 2 2025

Topic 2 Assignment (Homework) INSTRUCTOR

Summer Zwanziger Elsinger Grand Canyon University, AZ

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Grades Communication

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Current Score:  2 / 84 POINTS | 2.4 %

Scoring and Assignment Information

Due Date:  THU, JUL 31, 2025 4:00 AM CDT REQUEST EXTENSION

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) =

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