Question

**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 $0.46, on one serving of Dial 911, $0.59. Each serving of Wimpy requires 0.26 pound of beef, 0.26 cup of onions, and 6 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.26 pound of beef, 0.41 cup of onions, 3 ounces of Kilgore's special sauce, and 6 ounces of hot sauce. Today, Kilgore has 21 pounds of beef, 16 cups of onions, 89 ounces of Kilgore's special sauce, and 61 ounces of hot sauce on hand.

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)

a) max ___________ W+ _____________D

st

+ _________W+ ___________D >, <, or = _____________ Beef

+ _________W+ ___________D >, <, or = _____________ Onions

+ _________W+ ___________D >, <, or = _____________ Special sauce

+ _________W+ ___________D >, <, or = _____________ Hot Sauce

W,D >= 0

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

W = ___________, D = ___________, Profit = __________$

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

$ _________________

Interpret the shadow price and explain:

_________________________________________________________________

d. 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)? yes or no?

Answer #1

a)

W | D | ||

Max | 0.46 | 0.59 |

s.t | |||||

(beef) | 0.26 | 0.26 | <= | 21 | |

(onions) | 0.26 | 0.41 | <= | 16 | |

(special sauce) | 6 | 3 | <= | 89 | |

(Hot sauce) | 6 | <= | 61 |

b)

using excel, solver,

W | D | ||||

Max | 0.46 | 0.59 | |||

Quantity | 9.75 | 10.16667 | 10.48333333 | ||

s.t | |||||

(beef) | 0.26 | 0.26 | 5.178333333 | <= | 21 |

(onions) | 0.26 | 0.41 | 6.703333333 | <= | 16 |

(special sauce) | 6 | 3 | 89 | <= | 89 |

(Hot sauce) | 6 | 61 | <= | 61 |

W | 9.75 |

D | 10.17 |

Profit | 10.48 |

c) shadow price for special sauce = 0.08

d)

W=9.92

D=10.17

profit=10.48*1+0.08=10.56

answer: YES

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