Math, microeconomics

Question

Minimize c = −x + 7y subject to

y ≤ 2x / 3

x ≤ 3y

y ≥ 4

x ≥ 6

x + y ≤16

C =?

(x,y)= ?

Answer 1

graph the lines

shade in the areas that apply

find corner points of the shaded triangular area

(x,y) = (12,4), (6,4) or (9.6,6.4)

minimum Cost is at the corner point (12,4)

at (9.6,6.4) C=35.2, at (6,4) C=22

at (12,4)

C =-x+7y = -12+7(4) = 16 which is <22 or 35.2