Question

Find the minimum value of c=x+y subject to the following constraints 2x+y>=20, 2x+3y>=0, x>=0, y>=0

Answer 1

10

Explanation:

You want the minimum value of c = x +y, subject to the constraints {2x +y ≥ 20, 2x +3y ≥ 0, x ≥ 0, y ≥ 0}.

Graph

The attached graph shows the relevant vertices of the feasible region are (0, 20) and (10, 0). The value of c is minimized when (x, y) = (10, 0). At that point, c = 10 + 0 = 10.

The minimum value of c is 10.