Chapter 8.6, Problem 11E

In Exercises 5-14, an objective Junction and a system of linear inequalities representing constraints are given.

a. Graph the system of inequalities representing the constraints.

b. Find the value of the objective function at each corner of the graphed region.

c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

Objective Function Constraints

$\begin{array}{l}z=4x+2y\\ \{\begin{array}{l}x\ge 0,y\ge 0\\ 2x-3y\le 12\\ 3x-2y\le 12\\ x+y\ge 2\end{array}\end{array}$