Chapter 4, Problem 7P

a)

Summary Introduction

To formulate: A linear programming model and solve using a computer.

Explanation of Solution

Formulation:

Let ‘x’ be Apple Butter.

Let ‘y’ be Applesauce.

Let ‘z’ be Apple Jelly.

$\begin{array}{c}\text{Maximize}=190x+170y+155z\\ \text{Subject to}:\\ 3.5x+5.2y+2.8z\le 500\\ 1.2x+0.8y+1.5z\le 240\\ 40x+55y+20z\le 6,500\\ x,y,z\ge 0\end{array}$

Model and formulas:

Solver input:

Output:

b)

Summary Introduction

To explain: The impact on the model and the solution.

Explanation of Solution

Impact on the model and solution:

The leftover apples are 2,309.52. It will lead to additional revenue of

$\begin{array}{c}\text{Apple revenue}=2,309.52\times 0.08\\ =\$184.76\end{array}$

The leftover apple will lead to additional revenue of $184.76. There will not be any change in the model or the optimal solution.

c)

Summary Introduction

To explain: If Company F should use all the apples to produce cider along with the other three products.

Explanation of Solution

The idea of a new product:

The idea of producing the new product is not possible because even though there are leftover apples, Company F does not have any labor hours or cooking time available to manufacture cider. Hence, the proposed idea is not possible.