Chapter EP, Problem 3.4.6EP

To determine

The representation of the system of inequalities and the coordinates of the vertices of the feasible region. The maximum and minimum value of the function for the region.

Answer to Problem 3.4.6EP

The maximum value is $32$ and the minimum value is $0$ .

Explanation of Solution

Given information:

The inequality equation are:

  $\begin{array}{l}y\ge 0\\ 3x-2y\ge 0\\ x+3y\le 11\\ 2x+3y\le 16\end{array}$

Calculation:

The inequality equation are:

  $\begin{array}{l}y\ge 0\\ 3x-2y\ge 0\\ x+3y\le 11\\ 2x+3y\le 16\\ f(x,y)=4x+y\end{array}$

Graphing the three inequalities, the coordinates of the vertices would be:

  $\text{(2,3),(5,2),(8,0),(0,0)}$

The system of inequalities is bounded.

Now, evaluate the function using the coordinates found in the graph.

Thus, the maximum value is $32$ and the minimum value is $0$ .