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.

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 22 pounds of beef, 26 cups of onions, 87 ounces of Kilgore’s special sauce, and 56 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
Max W + D
s.t.
W + D (Beef)
W + D (Onions)
W + D (Special Sauce)
D (Hot Sauce)
WD 0

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 = $

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

Dual value for special sauce = $

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 = $

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

Expert Answer

 

W D
Profit 0.75 0.54 0 Maximization
Beef 0.2 0.2 0 <= 22 Constrains
Onions 0.2 0.32 0 <= 26
Spl Sauce 5 2 0 <= 87
Hot Sauce 0 4 0 <= 56

On solving for integer values of W and D

W D
12 13
Profit 0.75 0.54 16.02 Maximization
Beef 0.2 0.2 5 <= 22 Constrains
Onions 0.2 0.32 6.56 <= 26
Spl Sauce 5 2 86 <= 87
Hot Sauce 0 4 52 <= 56
W D Profit
12 13 16.0

On Increasing speacial sauce.

W D
12 14
Profit 0.75 0.54 16.56 Maximization
Beef 0.2 0.2 5.2 <= 22 Constrains
Onions 0.2 0.32 6.88 <= 26
Spl Sauce 5 2 88 <= 88
Hot Sauce 0 4 56 <= 56
W D Profit
12 14 16.6
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