Find the minimum value of z = 2x + 3y subject to the constraints?

Question

Find the minimum value of z = 2x + 3y subject to the constraints
5x + 3y > or = 15
x + 6y > or = 12
x > or = 0, y > or = 0


a) 5
b) 7
c) 9
d) 11

Answer 1

Plot the lines 5x + 3y = 15, x + 6y = 12, x = 0, and y = 0. Notice that these lines intersect at (2,5/3), (0,5), and (3,0). The region satisfying the four constraints is the area above those two skew lines and in the first quadrant.

Evaluate z at the intersection points and find that the minumum is 9.