how do you do this?

Question

Consider the region in the xy-plane defined the following set of linear inequalities.

x≥0, y≥0 x≤10

x+y≥5, x+2y≤18

1) Find the vertices of the feasible region.

2) What is the maximum and the minimum value of the function Q = 70x + 82y on the feasible region?

Answer 1

Hi Danielle, plotting the five inequalities give the following points that outline the feasible region:

(5,0), (10, 0), (10, 4), (0, 5), and (0, 9).

To find the maximum and minimum value of the function: Q = 70x + 82y, plug in each point and observe the results.

Q(5, 0) = 70(5) + 82(0), or 350

Q(10, 0) = 70(10) + 82(0), or 700

Q(10, 4) = 70(10) + 82(4), or 1020

Q(0, 5) = 70(0) + 82(5), or 410

Q(0, 9) = 70(0) + 82(9), or 738

Looking at the results, the maximum is 1020 at the point Q(10, 4), and the minimum is 350 at the point Q(5, 0).

Questions?