Math, microeconomics

Question

Minimize c = x + 2y subject to

x + 4y ≥ 28

2x + y ≥ 28

x ≥ 0, y ≥ 0.

c = ?

(x,y) = ?

Answer 1

x +4y = 28 endpoints (0,7) and (28,0)

2x +8y =56

2x +y = 28 endpoints (0,28), (14,0)

subtract

7y = 28

y=28/7 = 4

x = 28-4(4) = 12

(12,4) is a potential point of minimum cost

c=x+2y= 12+2(4) = 20

try the other end points, vertexes of the boundary lines

c(0) = 2(28) =56

c(28) = 28+0= 28

(12,4) is the cost minimizing point with c= 20