Chapter 11.8, Problem 8AYU

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.

$z=7x+5y$

To determine

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

Answer to Problem 8AYU

Solution:

Maximum value is 65 and Minimum value is 15.

Explanation of Solution

Given:

$z=7x+5y$

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
$\left(0,6\right)$	30
$\left(5,6\right)$	65
$\left(0,3\right)$	15
$\left(5,2\right)$	45
$\left(4,0\right)$	28

From the table, the maximum value is 65 and the minimum value is 15.