Chapter 7.5, Problem 65E

To determine

To sketch: the graph of inequalities that describes all possible production levels.

Explanation of Solution

Given information:

A furniture company produces tables and chair. Each table requires 1 hour in the assembly center and $1\frac{1}{3}$ hours in the finishing center. Each chair requires $1\frac{1}{2}$hours in the assembly center and $1\frac{1}{2}$hours in the finishing center. The assembly center is available 12 hours per day, and the finishing center is available 15 hours per day, and the finishing center is available 15 hours per day.

Calculation:

Consider the number of tables and number of chairs be $x$ and $y$ respectively.

Therefore, the number of hours to assemble the chair and tables $=x+\frac{3}{2}y$

The assembly center is available 12 hours per day. Therefore,

  $x+\frac{3}{2}y\le 12$

The number of hours in finishing of the chair and tables $=\frac{4}{3}x+\frac{3}{2}y$

The finishing center is available 15 hours per day. Therefore,

  $\frac{4}{3}x+\frac{3}{2}y\le 15$

Also, $x$ and $y$are positive. Therefore, the system of inequalities is,

  $\begin{array}{c}x+\frac{3}{2}y\le 12\\ \frac{4}{3}x+\frac{3}{2}y\le 15\\ x\ge 0\\ y\ge 0\end{array}$

The graph of the system of inequalities is shown below.

  

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