Chapter 8.6, Problem 27PE

A manufacturer produces two models of a gas grill. Grill $\text{A}$ requires $1\text{ hr}$ for assembly and $0.4\text{ hr}$ for packaging. Grill $\text{B}$ requires $1.2\text{ hr}$ for assembly and $0.6\text{ hr}$ for packaging. The production information and profit for each grill are given in the table. (See Example 4)

The manufacturer has $1200\text{ hr}$ of labor available for assembly and $540\text{ hr}$ of labor available for packaging.

a. Determine the number of grill $\text{A}$ units and the number of grill $\text{B}$ units that should be produced to maximize profit assuming that all grills will be sold.

b. What is the maximum profit under these constraints?

c. If the profit on grill $\text{A}$ units is $\text{\$}110$ and the profit on grill $\text{B}$ units is unchanged, how many of each type of grill unit should the manufacture produce to maximize profit?