What is the minimum value for p=x-2y over the feasibility region defined by the constraints shown above? x < = 8 y> = 0 y< = 3x+2 y< = -x+10 a. 8 b. -2 c. -16 d. -14

We want to minimize p=x-2y, given the constraints. This means we want x to be as small as possible and y to be as large as possible, since this will minimize p. 

The fact that x ≤ 8 and y ≥ 0 means we are free to set x as low and y as high as possible, as long as they agree with the other constraints.

Graphing the inequalities helps to see the optimum point. It is where 3x +2 and   -x +10 intersect, at (2,8). This is the greatest point for y that agrees with our inequality.

Remember that the function we are minimizing is p = x - 2y
The value for p at this point is 2 - 2(8) = 2 - 16 = -14

Answer is D)