Chapter 8.6, Problem 28PE

A manufacturer produces two models of patio furniture. Model $\text{A}$ requires $2\text{ hr}$ for assembly and $1.2\text{ hr}$ for painting. Model $\text{B}$ requires $3\text{ hr}$ for assembly and $1.5\text{ hr}$ for painting. The production information and profit for selling each model are given in the table.

The manufacturer has $1200\text{ hr}$ of labor available for assembly and $660\text{ hr}$ of labor available for painting.

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

b. What is the maximum profit under these constraints?

c. If the profit on model $\text{A}$ units is $\text{\$}180$ and the profit on model $\text{B}$ units remains the same, how many of each type should the manufacturer produce to maximize profit?