Question

Guys please help me solve this I’m struggling

Answer 1

Answer:

$Max\ z = 1$

$Min\ z = -9$

Step-by-step 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:

$Max\ z = 1$

$Min\ z = -9$