Answer:
Minimum = 0
Maximum = 15
Step-by-step explanation:
Given
Optimization Equation: [tex]z = 2x + 5y[/tex]
Constraints:
[tex]2x- y \le 12[/tex]
[tex]4x + 2y \ge 0[/tex]
[tex]x + 2y \le 6[/tex]
[tex]x,y\ge 0[/tex]
Required
The maximum and the minimum values of z
To do this, we make use of graphical method.
Plot the constraints on a graph (see attachment)
Get the corner points from the points.
These are the points where [tex]x,y\ge 0[/tex]
So, we have:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (0,3)[/tex]
[tex](x_3,y_3) = (6,0)[/tex]
Substitute these points in the optimization equation:
[tex](x_1,y_1) = (0,0)[/tex]
[tex]z = 2x + 5y[/tex]
[tex]z = 2 * 0 + 5 * 0 = 0[/tex]
[tex](x_2,y_2) = (0,3)[/tex]
[tex]z = 2 * 0 + 5 * 3 = 15[/tex]
[tex](x_3,y_3) = (6,0)[/tex]
[tex]z = 2 * 6 + 5 * 0 = 12[/tex]
So, the values are:
Minimum = 0
Maximum = 15
