Mathematics: Given the following constraints, find the maximum and minimum values for z. Constraints: 2x−y≤124x+2y≥0x+2y≤6 Optimization Equation: z=2x+5y

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Given the following constraints, find the maximum

keishonnawimbush

22.08.2021

Minimum = 0

Maximum = 15

Step-by-step explanation:

Given

Optimization Equation: z = 2x + 5y

Constraints:

$2x- y \le 12$

$4x + 2y \ge 0$

$x + 2y \le 6$

$x,y\ge 0$

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 $x,y\ge 0$

So, we have:

(x_1,y_1) = (0,0)

(x_2,y_2) = (0,3)

(x_3,y_3) = (6,0)

Substitute these points in the optimization equation:

(x_1,y_1) = (0,0)

z = 2x + 5y

z = 2 * 0 + 5 * 0 = 0

(x_2,y_2) = (0,3)

z = 2 * 0 + 5 * 3 = 15

(x_3,y_3) = (6,0)

z = 2 * 6 + 5 * 0 = 12

So, the values are:

Minimum = 0

Maximum = 15

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