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 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 Kilgore’s special sauce. Each serving of

Dial 911 requires .25 pound of beef, .4 cup of onions, 2 ounces of Kilgore’ s special sauce,

and 5 ounces of hot sauce. Today, Kilgore has 20 pounds of beef, 15 cups of onions, 88

ounces of Kilgore’s 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 solu

tion confirm the answer to part (c)? Give the new solution.

Show step by step solution of each sub part by using excel solver

Answer 1

Concepts and reason

Linear programming:

Linear programming is a simple way to optimize a system. It aids in solving complex optimization problems by making simple and logical assumptions. It is the method followed to achieve the best outcome for a problem.

Objective function: The profit contribution for the jobs will be the objective function. The objective is to maximize the profit.

Fundamentals

The general format of LPP problem is,

Subject to constraints:

Instructions for MS Excel solver:

1.Enter all the data as shown below.

2.Under data tab in MS Excel click solver.

3.Enter the respective formula for each cell.

4.Enter the solver parameters as shown below.

5.Click the solve button.

(a)

The formulation of linear programing problem is determined as shown below:

Let ‘x’ be number of Wimpy servings.

Let ‘y’ be number of Dial 911 servings.

(b)

Instructions for obtaining the optimal solution using Solver:

1.Input the given data as shown in the excel form.

2.Enter the corresponding formula for each cell as shown below.

3.Fill in the solver parameter details as shown below.

4.Click ‘solve’ to get the solver results for the optimal solution.

Excel result:

Excel Formula:

Solver parameters:

From solver output, the optimal solution is,

(c)

The sensitivity report is determined below:

The sensitivity report is obtained by clicking the sensitivity button in the solver results tab and then clicking “ok”.

The shadow price for hot sauce is $.0.08. It means there will be a profit increase of $0.08 for every 1-ounce increase of hot sauce in the total available resources.

(d)

The new optimal solution is obtained as shown below:

The increase in the available resources of hot sauce as increased the profit by $0.08. The new total profit is $12.80.

New optimal solution is,

Wimpy (x) = 12.72

Dial 911 (y) = 12.2

Total profit = $12.80

Ans: Part a

Thus, the linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today is,