1 Answer

Alcedine · Answer 1 · 2022-03-31T13:10:20+0000

Answer:

$Max\ z = 1$

$Min\ z = -9$

Explanation:

Given

z = 4x + 5y

$x \ge -1$

$y \le 2x +3$

$y \le -1$

Required

The maximum and minimum of z

To do this, we make use of the graphical method

See attachment for graphs of

$x \ge -1$

$y \le 2x +3$

$y \le -1$

The corner points of the function are:

(x,y) = (-1,1)

(x,y) = (-1,0)

(x,y) = (-1,-1)

We have:

z = 4x + 5y

Calculate z with the above values

z = 4(-1) + 5(1) = 1

z = 4(-1) + 5(0) = -4

z = 4(-1) + 5(-1) = -9

So, we have:

$Max\ z = 1$

$Min\ z = -9$

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