Chapter SH, Problem 3.8EP

To determine

To graph the given system of inequalities, name the coordinates of the feasible region and find the maximum and minimum value of the given functions for this region.

Explanation of Solution

Given:

The given system of inequalities are −

  $\begin{array}{l}x\ge -2\\ y\le 4\\ y\ge x-1\\ f(x,y)=2x-y\end{array}$

Calculation:

The graph of the inequalities is shown below-

  

From the graph the vertices of feasible region are $(-2,4),(5,4),(-2,-3)$ .

Now evaluate the given function $f(x,y)=2x-y$ at each vertex as follows-

  $\begin{array}{l}f(-2,4)=2(-2)-4=-8\\ f(5,4)=2(5)-4=6\\ f(-2,-3)=2(-3)-4=-10\end{array}$

Hence the maximum value is $6$ and the minimum value is $-10$