Problem

Kilgores Deli is a small delicatessen located near a major university. Kilgores 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, .25 cup of onions, and 5 ounces of Kilgores special sauce. Each serving of Dial 911 requires .25 pound of beef, .4 cup of onions, 2 ounces of Kilgores special sauce, and 5 ounces of hot sauce. Today, Kilgore has 20 pounds of beef, 15 cups of onions, 88 ounces of Kilgores special sauce, and 60 ounces of hot sauce on hand.

a. 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.

b. Find an optimal solution.

c. What is the shadow price for special sauce? Interpret the shadow price.

d. Increase the amount of special sauce available by 1 ounce and re-solve. Does the solution confirm the answer to part (c)? Give the new solution.