Question

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 e. 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 beef, 0.45 cup of onions, and 5 ounces of Kllgore's special sauce. Each serving of Dial 911 requires on one serving of Dial 911, $0.55. Each serving of Wimpy requires 0.45 pound 0.45 pound of beef, 0.72 cup of onions, 1 ounces of Kilgore's special sauce, and 7 ounces hot sauce. Today, Kilgore has 37 pounds of beef, 46 cups of onions, 93 ounces of Kilgore's special sauce, and 98 ounces hot sauce on hand a. 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 # of servings of Wimpy to make W = D = of servings of Dial 911 to make Max D S.t Beef) D (Onions) Special Sauce) D Hot Sauce) D W, D b. Find an optimal solution. Round the answer for profit to the nearest cent and, if required, round the answers for Wand to one decimal place. Solution: W Profit $ D c. What is the dual value for special sauce? Round your answer to the nearest cent. Dual value for special sauce $ ounce. Give the new solution. Round the answer for profit to the nearest cent d. Increase the amount of special sauce available by D = Profit $ Solution: W=

Answer 1

a)

Let,

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

Objective is to maximize profit so objective function = Max 0.45W + 0.55D

Subject to,

0.45W + 0.45D <= 37 (Beef)

0.45W + 0.72D <= 46 (Onions)

5W + 1D <= 93 (Special sauce)

7D <= 98 (Hot sauce)

W,D >= 0 (Non-negativity constraint)

b)

Solution: W = 15.8, D = 14, Profit = $14.81

C D G 1 2 W D 15.8 Objective function 14. 14.81 4 5 Beef 0.45 0.45 13.41= 37 6 Onions 0.45 0.72 17.19 <= 46 7 Special Sauce 5 1 93 <= 93 Hot Sauce 7 98 98 10 T co

c)

Sensitivity report

5 6 Variable Cells Final Reduced Objective Allowable Allowable 7 Value Cell Coefficient 8 Name Cost Increase Decrease $B$3 W 15.8 0 0.45 2.3 0.45 $C$3 D 1E+30 10 14 0 0.55 0.46 11 12 Constraints Final Shadow Constraint Allowable Allowable 13 Cell Value Price 14 Name R.H. Side Increase Decrease $D$5 Beef 15 13.41 0 37 1E+30 23.59 $D$6 Onions 17.19 46 16 0 1E+30 28.81 $D$7 Special Sauce $D$8 Hot Sauce 17 93 0.09 93 262.1111111 79 18 98 0.065714286 98 320.1111111 98 19 20.

From the above sensitivity report we can see Dual value for Special sauce is $0.09 (Dual value is the shadow price)

d)

As the increase of 1 ounce of Special sauce is within allowable increase limit so the shadow price will remain valid So the profit will increase by 1*0.09 = 0.09 and new profit will be 14.81+0.09 = 14.9

Solution: W = 16, D = 14, Profit = $14.90