Question

x>=0
y<=8
y>=x
y>=-1/2x+6
What is the minimum value for over the feasibility region defined by the constraints shown above?%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A–4%0D%0A–4%0D%0A%0D%0A–5%0D%0A–5%0D%0A%0D%0A–3%0D%0A–3%0D%0A%0D%0A–6

Answer 1

To find the minimum value for y over the feasibility region, we need to find the minimum value for y in each of the given constraints.

First, we consider the constraint x >= 0. The minimum value for x in this constraint is 0. Therefore, y >= 0.

Next, we consider the constraint y <= 8. The maximum value for y in this constraint is 8. Therefore, y >= 8.

Next, we consider the constraint y >= x. Since x >= 0, the minimum value for y in this constraint is also 0. Therefore, y >= 0.

Finally, we consider the constraint y >= -1/2x + 6. Since x >= 0, the maximum value for y in this constraint is when x = 0. Plugging x = 0 into the equation, we get y >= 6.

Combining all the constraints, we find that the minimum value for y is 8.

Therefore, the minimum value for y over the feasibility region defined by the constraints is 8.