Question

What is the minimum value for z 3x 1 2y over the feasibility region defined by the constraints shown below?x>0y<8y>xy>-1/2x 6

Answer 1

Explanation:

My answer is:

The constraints are x≥0, y≤8, y≥x and y≥
`-(1)/(2)+6`.

(x,y)
`z=3x-(1)/(2)y`

(0,6)
`z=3(0)-(1)/(2)(6)=-3`

(0,8)
`z=3(0)-(1)/(2)(8)=-4`

(4,4)
`z=3(4)-(1)/(2)(4)=10`

(8,8)
`z=3(8)-(1)/(2)(8)=20`

The minimum value is -3 or -4. -3 occurs at (0,6) And -4 occurs at (0,8). I'm putting -3 as my answer on my test and I'll post the correct answer if its wrong.

Answer 2

The minimum value for z = 3 x - 1/2 y over the feasibility region is where x has the minimum value and y has the maximum value.
x ≥ 0, y ≤ 8, y ≥ x and y ≥ - 1/2 x + 6
Those values are: x = 0 and y = 8
z min = 3 · 0 - 1/2 · 8 = 0 - 4 = - 4
Answer: A ) - 4