Answered Essay: 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

Problem 4-05 (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 $0.75, on one serving of Dial 911, $0.54. Each serving of Wimpy requires 0.2 pound of beef, 0.2 cup of onions, and 5 ounces of Kilgore’s special sauce. Each serving of Dial 911 requires 0.2 pound of beef, 0.32 cup of onions, 2 ounces of Kilgore’s special sauce, and 4 ounces of hot sauce. Today, Kilgore has 12 pounds of beef, 16 cups of onions, 76 ounces of Kilgore’s special sauce, and 44 ounces of hot sauce on hand.

Develop an LP model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today.

Let
W = # of servings of Wimpy to make
D = # of servings of Dial 911 to make

a.

Max W + D
s.t.
W + D (Beef)
W + D (Onions)
W + D (Special Sauce)
D (Hot Sauce)
WD

​b.Find an optimal solution. Round the answer for profit to the nearest cent and, if required, round the answers for W and D to one decimal place.

Solution: W = , D = , Profit = $

c.What is the dual value for special sauce? Round your answer to the nearest cent.

Dual value for special sauce = $

d. Increase the amount of special sauce available by 1 ounce. Give the new solution. Round the answer for profit to the nearest cent.

Solution: W = , D = , Profit = $

Expert Answer

 

Formulation:

Max $0.75W + $0.54D
s.t.
0.2W + 0.2D 12 (Beef)
0.2W + 0.3D 16 (Onions)
5W + 2D 76 (Special Sauce)
4D 44 (Hot Sauce)
WD    0 (Non-negative)

Spreadsheet Model and Solver Solution:

b.Find an optimal solution.

Solution: W = 10.8, D = 11, Profit = $ 14.04

Sensitivity Report:

c.What is the dual value for special sauce?
Dual value of constraint is shadow price.
Dual value for special sauce = $0.15    (cell E17)

It means the profit will improve by 0.15 if additional ounce of special sauce is made available or vice versa.

d. Increase the amount of special sauce available by 1 ounce. Give the new solution.

Solution: W = 11, D = 11, Profit = $14.19

With the increase in the amount of special sauce by 1 ounce, the profit is increased by $0.15.

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