Question

Find the minimum value of

C = x+y
subject to the following constraints:
2x + y 2 20
2x + 3y2 36
x20
(y20
C = [?]
Enter
What does C equal?? PLEASE HELP WILL GIVE LOTS OF POINTS!!!

Answer 1

C = 14

Explanation:

`C = x+y`

`2x + y \geq 20`

`2x + 3y\geq 36`

`x\geq 0`

`y\geq 0`

If we graph the inequalities, the solution set of the constraints is the shaded area (see attached diagram).

The vertices of the shaded area are (0, 20), (6, 8) and (18, 0)

To determine the minimum value of C, substitute the values of x and y of each vertex into C = x + y:

at (0, 20): C = 0 + 20 = 20

at (6, 8): C = 6 + 8 = 14

at (18, 0): C = 18 + 0 = 18

Therefore, the minimum value is at (6, 8) ⇒ C = 14