Question

Instructions: Given the following constraints, find the maximum and minimum values for

z
.

Constraints: 2−≤124+2≥0+2≤6 2x−y≤12 4x+2y≥0 x+2y≤6
Optimization Equation: =2+5
z
=
2
x
+
5
y
Maximum Value of
z
:
Minimum Value of
z
:

Answer 1

z(max) = 16

z(min) = -24

Explanation:

2x - y = 12 multiply by 2

4x - 2y = 24 (1)

4x + 2y = 0 add equations

8x = 24

x = 3

4(3) + 2y = 0

y = -6

so (3, -6) is a common point on these two lines

z = 2(3) + 5(-6) = -24

4x - 2y = 24 (1)

x + 2y = 6 add equations

5x = 30

x = 6

6 + 2y = 6

y = 0

so (6, 0) is a common point on these two lines

z = 2(6) + 5(0) = 12

4x + 2y = 0 multiply by -1

-4x - 2y = 0

x + 2y = 6 add equations

-3x = 6

x = -2

-2 + 2y = 6

y = 4

so (-2, 4) is a common point on these two lines

z = 2(-2) + 5(4) = 16