Question

In: Economics

Problem 9-05 (Algorithmic) Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does...

Problem 9-05 (Algorithmic)

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 $0.51, on one serving of Dial 911, $0.69. 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, 0.38 cup of onions, 2 ounces of Kilgore’s special sauce, and 5 ounces of hot sauce. Today, Kilgore has 25 pounds of beef, 20 cups of onions, 75 ounces of Kilgore’s special sauce, and 53 ounces of hot sauce on hand.

  1. 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)
    Let W = number of servings of Wimpy to make
    D = number of servings of Dial 911 to make
    Max W + fill in the blank 2D
    s.t.
    W + D    (Beef)
    W + D (Onions)
    W + D (Special Sauce)
    W + D (Hot Sauce)
    W, D 0
  2. Find an optimal solution. If required, round your answers to two decimal places.

    W = , D = , Profit = $
  3. What is the shadow price for special sauce? If required, round your answers to two decimal places.


    Interpret the shadow price.

    The input in the box below will not be graded, but may be reviewed and considered by your instructor.


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

    W = , D =   , Profit = $

    Does the solution confirm the answer to part (c)?

Solutions

Expert Solution

a)

Let

X1 = number of servings of Wimpy to make

X2 = number of servings of Dial 911 to make

X1

X2

Beef

0.24

0.24

5.9232

<=

19

Onions

0.24

0.39

7.6932

<=

14

SS

5

2

88

<=

88

HS

0

5

59

<=

59

Profit

0.44

0.57

12.3932

Decision Variables

12.88

11.8


Related Solutions

Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does a large walk-in...
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 $0.4, on one serving of Dial 911, $0.53. Each serving of Wimpy requires 0.2 pound of beef,...
Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does a large walk-in...
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 $0.4, on one serving of Dial 911, $0.53. Each serving of Wimpy requires 0.2 pound of beef,...
Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does a large walk-in...
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 $0.41, on one serving of Dial 911, $0.54. Each serving of Wimpy requires 0.21 pound of beef,...
Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does a large walk-in...
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 $.45, on one serving of Dial 911, $.58. Each serving of Wimpy requires .25 pound of beef,...
Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does a large walk-in...
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 $0.42, on one serving of Dial 911, $0.55. Each serving of Wimpy requires 0.22 pound of beef,...
Kilgore's Deli is a small delicatessen located near a major university. Kilgore's does a large walk-in...
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 $0.45, on one serving of Dial 911, $0.58. Each serving of Wimpy requires 0.25 pound of beef,...
Kilgore's Deli is a small delicatessen located near a major university. Kilgore does a large walk-in...
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 $0.35, on one serving of Dial 911, $0.59. Each serving of Wimpy requires 0.45 pound of beef,...
Problem 16-05 (Algorithmic) A major traffic problem in the Greater Cincinnati area involves traffic attempting to...
Problem 16-05 (Algorithmic) A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.9 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75. Traffic is classified as having either a delay or...
Problem 16-05 (Algorithmic) A major traffic problem in the Greater Cincinnati area involves traffic attempting to...
Problem 16-05 (Algorithmic) A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.8 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.65. Traffic is classified as having either a delay or...
Problem 16-05 (Algorithmic) A major traffic problem in the Greater Cincinnati area involves traffic attempting to...
Problem 16-05 (Algorithmic) A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.8 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.65. Traffic is classified as having either a delay or...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT