Chapter 11.8, Problem 4AYU

In problems 3-8, find the maximum and minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points.

$z=2x+3y$

To determine

To find: The maximum and minimum value of given objective function of a linear programming problem.

Answer to Problem 4AYU

Solution:

Maximum value is 28 and Minimum value is 8.

Explanation of Solution

Given:

$z=2x+3y$

From the graph, the corner points are $\left(0,6\right),\left(5,6\right),\left(0,3\right),\left(5,2\right),\left(4,0\right)$.

Calculation:

The below table lists the corner points and the corresponding values of objective function.

Corner points are	Value of objective function
$\left(0,6\right)$	18
$\left(5,6\right)$	28
$\left(0,3\right)$	9
$\left(5,2\right)$	16
$\left(4,0\right)$	8

From the table, the maximum value is 28 and the minimum value is 8.