Chapter 2.7, Problem 8CFU

To determine

To find: the number of each loaf should the bakery make. and if not possible then state whether this situation is infeasible, has alternate optimal solutions, or is unbounded.

Answer to Problem 8CFU

Infeasible

Explanation of Solution

Given information:

Flour required for preparing light wheat loaf = 2 cups

Flour required for preparing regular wheat loaf = 3 cups

Eggs required for preparing light wheat loaf = 1

Eggs required for preparing regular wheat loaf = 2

Total flour = 90 cups

Total eggs = 80

Profit on light bread per loaf= $1

Profit on regular bread per loaf= $1.50

Calculation:

Let light bread and regular bread be x and y respectively. The inequalities derived from the data are as follows:

  $\begin{array}{l}2x+3y\le 90\\ x+2y\le 80\end{array}$

The function for maximizing profit is as follows:

  $f\left(x,y\right)=x+1.50y$

The graph for the given inequalities is as follows:

  

Since two inequalities create solution ranges that do not overlap. So finding $f\left(x,y\right)$ for a maximum is infeasible.