BUS 660 Week 4 Linear Programming Applications in Marketing, Finance, and Marketing Management – Homework

(BUS 660 Week 4 Linear Programming Applications)

Problem 9-07 (Algorithmic)

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):

Assume that interest is paid annually. The plan will … to the judge and, if … , Hoxworth will … to pay a trustee the amount that will be required to fund the plan.

1. Use linear programming to find the minimum cash settlement necessary to fund the annual payments.
2. Note: All decision variables are … in thousands of dollars. If … , round your answers to five decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
3. Round your answer to the nearest dollar. If an amount is zero, enter “0”.
5. Use the dual value to determine how much more 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.
6. Use the dual value to determine how much more Hoxworth should be willing to pay to reduce the year 1 payment to $150,000. Round your answer to the nearest dollar.
7. Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change. Note: All decision variables are … in thousands of dollars. If … , round your answers to five decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
8. How much would Hoxworth save if this change could be … ? Round your answer to the nearest dollar.

Problem 9-17: Frandec Company manufactures, assembles, and rebuilds material handling equipment … in warehouses and distribution centers. One product, … a Liftmaster, is … from four components: a frame, a motor, two supports, and a metal strap. Frandec’s production schedule calls for 5000 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.

Three departments are … in the production of these components. The time (in minutes per unit) … to process each component in each department and the available capacity (in hours) for the three departments are as follows:

1. Formulate and solve a linear programming model for this make-or-buy application. How many of each component should … and how many should … ? If required, round your answers to one decimal place.
3. FM, FP, SM, SP, TM, TP ≥ 0.
4. What is the total cost of the manufacturing and purchasing plan? When … , round your answer to the nearest dollar.
7. How many hours of production time are …in each department?
8. How much should Frandec be willing to pay for an additional hour of time in the shaping department?
9. Another manufacturer has …to sell frames to Frandec for $45 each. Could Frandec improve its position by pursuing this opportunity?
10. The input in the box below will not … , but may …  by your instructor.

Problem 9-15

Bay Oil produces two types of fuels (regular and super) by mixing three ingredients. The major distinguishing feature of the two products is the octane level … Regular fuel must have a minimum octane level of 90 while super must have a level of at least 100. The cost per barrel, octane levels, and available amounts (in barrels) for the upcoming two-week period are shown in the following table. Likewise, the maximum demand for each end product and the revenue … per barrel are shown.

Develop and solve a linear programming model to maximize contribution to profit. Let Ri = the number of barrels of input i to use to produce Regular, i=1,2,3

Si = the number of barrels of input i to use to produce Super, i=1,2,3

If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

Problem 9-09 (Algorithmic)

Epsilon Airlines services predominantly the eastern and southeastern united States. The vast majority of Epsilon’s customers make reservations through Epsilon’s website, but a small percentage of customers make reservations via phones. Epsilon employs call center personnel to handle these reservations and to deal with website reservation system problems and for the rebooking of flights for customers whose plans have …or whose 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 … the minimum number of call center employees … by day of the week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are as follows:

Problem 9-13 (Algorithmic)

Romans Food Market, … in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store’s leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are … from a distributor …in New York City. Because Romans purchases large quantities, the coffee beans may … on an as-needed basis for a price 10% higher than the market price the distributor pays for the beans. The current market price is $0.46 per pound for Brazilian Natural and $0.64 per pound for Colombian Mild. The compositions of each coffee blend are as follows:

Problem 9-05 (Algorithmic)

Kilgore’s Deli is a small delicatessen …near a major university. Kilgore’s 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 $0.41, on one serving of Dial 911, $0.54.

Each serving of Wimpy requires 0.21 pound of beef, 0.21 cup of onions, and 5 ounces of Kilgore’s special sauce. Each serving of Dial 911 requires 0.21 pound of beef, 0.36 cup of onions, 2 ounces of Kilgore’s special sauce, and 5 ounces of hot sauce. Today, Kilgore has 16 pounds of beef, 11 cups of onions, 85 ounces of Kilgore’s special sauce, and 56 ounces of hot sauce on hand.

Problem 9-01

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 newspaper. Audience estimates, costs, and maximum media usage limitations are as shown:

To ensure a … use of advertising media, radio advertisements must not … 50% of the total number of advertisements … In addition, television should account for at least 10% of the total number of advertisements authorized.

Problem 9-11

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have … 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:

Each supplier has a … 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 … is within its capacity. Supplier capacities are as follows:

If the Edwards production plan for the next period includes 1000 units of component 1 and 800 units of component 2, what purchases do you recommend? That is, how many units of each component should … from each supplier?

(BUS 660 Week 4 Linear Programming Applications, BUS 660 Week 4 Linear Programming Applications)