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HomertheGenius

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

QueasyUnicorn14

Answer:

Step-by-step explanation:

My answer is:

The constraints are x≥0, y≤8, y≥x and y≥\(-\frac{1}{2}+6\).

(x,y)           \(z=3x-\frac{1}{2}y\)

(0,6)          \(z=3(0)-\frac{1}{2}(6)=-3\)

(0,8)          \(z=3(0)-\frac{1}{2}(8)=-4\)

(4,4)          \(z=3(4)-\frac{1}{2}(4)=10\)

(8,8)          \(z=3(8)-\frac{1}{2}(8)=20\)

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.

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