Chapter 5.3, Problem 50E

In Problems 49-64, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve by the geometric method.

Furniture. A furniture manufacturing company manufactures dining-room tables and chairs. The relevant manufacturing data are given in the table below.

$\begin{array}{l}\begin{array}{ccc}& \begin{array}{l}\text{Labor-Hours }\\ \text{ per Unit}\end{array}& \end{array}\\ \begin{array}{cccc}\text{Department}& \text{Table}& \text{Chair}& \begin{array}{l}\text{Maximum Labor-Hours }\\ \text{Available per Day}\end{array}\\ \text{Assembly}& 8& 2& 400\\ \text{Finishing}& 2& 1& 120\\ \text{Profit per unit}& \text{\$}90& \text{\$}25& \end{array}\end{array}$

(A) How many tables and chairs should be manufactured each day to realize a maximum profit? What is the maximum profit?

(B) Discuss the effect of production schedule and the maximum profit if the marketing department of the company decides that the number of chairs produced should be at least four times the number of tables produced.