What is the shadow price for special sauce

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Reference no: EM132625330

Linear Programming: Applications in Marketing, Finance, and Marketing Management

Problem 1:

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	195	220	270	320	350	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 3.5% 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 = $1000). Funds not invested in these securities will be placed in savings.

Security	Current Price	Rate (%)	Years to Maturity
1	$1045	6.85	3
2	$1000	5.525	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 to fund the annual payments.
Let
F = total funds required to meet the six years of payments
G1 = units of government security 1
G2 = units of government security 2
Si = investment in savings at the beginning of year i

b.
Note: All decision variables are expressed in thousands of dollars.

If required, 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)

c. Round your answer to the nearest dollar. If an amount is zero, enter "0".

Current investment required	$
Investment in government security 1	$
Investment in government security 2	$
Investment in savings for year 1	$
Investment in savings for year 2	$
Investment in savings for year 3	$
Investment in savings for year 4	$
Investment in savings for year 5	$
Investment in savings for year 6	$

e. 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.

f. 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.

Hoxworth should be willing to pay anything less than $ .

g. 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 expressed in thousands of dollars.

If required, 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)

How much would Hoxworth save if this change could be negotiated? Round your answer to the nearest dollar.

Problem 2:

Romans Food Market, located 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 purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 12% higher than the market price the distributor pays for the beans. The current market price is $0.45 per pound for Brazilian Natural and $0.67 per pound for Colombian Mild. The compositions of each coffee blend are as follows:

	Blend
Bean	Regular	DeCaf
Brazilian Natural	60%	40%
Colombian Mild	40%	60%

Romans sells the Regular blend for $3.3 per pound and the DeCaf blend for $4.5 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 1100 pounds of Romans Regular coffee and 525 pounds of Romans DeCaf coffee. The production cost is $0.84 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.08 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit.
Let BR = pounds of Brazilian beans purchased to produce Regular
BD = pounds of Brazilian beans purchased to produce DeCaf
CR = pounds of Colombian beans purchased to produce Regular
CD = pounds of Colombian beans purchased to produce DeCaf
If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

The complete linear program is

What is the contribution to profit?

Problem 3:

Kilgore's Deli is a small delicatessen located 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 $0.47, on one serving of Dial 911, $0.6. Each serving of Wimpy requires 0.27 pound of beef, 0.27 cup of onions, and 7 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.27 pound of beef, 0.42 cup of onions, 4 ounces of Kilgore's special sauce, and 7 ounces of hot sauce. Today, Kilgore has 22 pounds of beef, 17 cups of onions, 90 ounces of Kilgore's special sauce, and 62 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. If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

d. Find an optimal solution. If required, round your answers to two decimal places.

e. What is the shadow price for special sauce? If required, round your answers to two decimal places.

f. Increase the amount of special sauce available by 1 ounce and re-solve. If required, round your answers to two decimal places.

Attachment:- Linear Programming.rar

Reference no: EM132625330

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