Question

Minimize and Maximize w = 3x + 8y subject to the constraints:

I > 0
y > 0
-y < -2
3x + y > 3
a) Minimize w = 3x + 8y
b) Maximize w = 3x + 8y
c) Find the value of w when I > 0, y > 0, -y < -2, and 3x + y > 3
d) None of the above

Answer 1

To minimize and maximize the function w = 3x + 8y, we need to find the feasible region by graphing the given inequalities and finding the intersection of the shaded regions. The corner points (vertices) of the feasible region will be the potential solutions. We can then plug these corner points into the objective function and compare the values to find the minimum and maximum.

Step-by-step explanation:

To minimize and maximize the function w = 3x + 8y, we need to find the feasible region by graphing the given inequalities and finding the intersection of the shaded regions. The corner points (vertices) of the feasible region will be the potential solutions. We can then plug these corner points into the objective function and compare the values to find the minimum and maximum.

In this case, the feasible region will be a quadrilateral. Graphing the inequalities, we find that the vertices are (0,0), (1,4), (3,1), and (3,0). Evaluating the objective function at these points, we find that the minimum is 24 and the maximum is 33.