LP Output Interpretation

1. The Cookie Store at a small shopping center makes three types of cookies—chocolate chip, pecan chip, and twists. The three main ingredients are chocolate chips, pecans, and sugar. The store has 312 pounds of sugar, 125 pounds of chocolate chips, and 50 pounds of pecans. At least 5 batches of chocolate chip cookies should be made.

The linear programming model has been developed as given below for determining the number of batches of chocolate chip cookies (x ₁ ), pecan chip cookies (x ₂ ), and twists (x ₃ ) to make in order to maximize profit.

Max z = 20x ₁ + 25x ₂ +17x ₃ dollars

Subject to:

21x ₁ + 15x ₂ + 9x ₃ \(\le \) 312 pounds of sugar

10x ₁ + 5x ₂ \(\le \) 125 pounds of chocolate chips

x ₁ + 2x2 \(\le \) 50 pounds of pecan

x _{1 \(\ge \)} 5 batches of chocolate chip cookies

x ₁ , x ₂ , x ₃ \(\le \) 0

Solve the problem using Excel Solver and answer the following.

1. How many batches of each type of cookie should be made? What is the total profit?
2. Which constraints are binding? Why?
3. What does s ₂ represent? (Slack or surplus). Explain what it means.
4. How many pounds of pecans are used?
5. Should the company make more batches of chocolate chip cookies? Why or why not?
6. How profitable should the pecan chip cookies be in order to make some?
7. What would the new total profit be if there were 7 additional pounds of sugar?
8. What would happen to the optimal solution to this problem if the profit per batch of chocolate chip cookies were increased to $24? Why? What would the new total profit of the store be?

2. DY Chemicals blends its famous, private label insect spray from four individual compounds. Management would like to make the blend at as low a cost as possible while maintaining the requirements for chemical structure. The linear programming problem formulation is given below.

With x _i = gallons of compound i in the blend; i =1, 2, 3, 4

Solve the problem using Excel Solver and answer the following.

1. How much of each compound is used? What is the total cost?
2. Which constraints are binding? Why?
3. What costs would each of the non-used compounds have to have in order to be used in the blend?
4. What does s 1 = 0 and s ₂ = 366.667 represent? (Slack or surplus). Explain what they mean.
5. How many gallons of chemical 2 are used in the process?
6. What would the new total cost be if the chemical 1 requirement were increased by 100 gallons?
7. Suppose the cost per unit for compound 1 were actually $7.25. How would the solution change (i.e., how much of each compound would be used) and why? How much would the total cost change?

Price: $11.61

Solution: The downloadable solution consists of 4 pages, 761 words and 1 charts.
Deliverable: Word Document