Chapter 7.6, Problem 44E

To determine

To find: the maximum and minimum values of $f\left(x,y\right)$ for polygon convex set determined by the system of inequalities.

Answer to Problem 44E

Maximum value = 16

Minimum value = 4

Explanation of Solution

Given information:

  $\begin{array}{c}f\left(x,y\right)=3x-y+4\\ x+y\le 8\\ y\ge 3\\ x\ge 2\end{array}$

Calculation:

Graph the inequalities by using graphing calculator and label the vertices as follows:

  

Now put the vertices in the $f\left(x,y\right)$ and test for the maximum and minimum values as shown below.

  $\begin{array}{c}f\left(2,3\right)=3\left(2\right)-3+4\\ =7\\ f\left(2,6\right)=3\left(2\right)-6+4\\ =4\\ f\left(5,3\right)=3\left(5\right)-3+4\\ =16\end{array}$

Thus, the maximum value is 16 and minimum value is 4.