Question

Q. Mark produces different sizes of Shoes to sell to tourists visiting Dubai. The big pair of shoes require 6 hours of making time whereas the small pair requires only two hour of making time. Similarly polishing times for big pair of shoes requires 3 hours while one hour for small pair. He has 36 hours for shoe making and 24 hours for shining. The smaller pair of shoes sell for $6 each, while the larger vases would bring $12 each. Let’s X₁ represents the small pairs and X₂ big pair of shoes.

1.   Formulate the linear Programing problem and solve for the profit maximization combination of pairs of shoes.

     (b) Graphically show the profit maximization bundle of shoes.

Answer 1

Part (a) Formulate the linear Programing problem and solve for the profit maximization combination of pairs of shoes.

Maximize, z = 6X1 + 12X2

subject to:

L1: 2X1 + 6X2 = 36

L2: X1 + 3X2 = 24

X1, X2 ≥ 0

Part (b) Graphically show the profit maximization bundle of shoes.

Profit maximization will occur either at point A (0, 6) or B (18, 0)

Profit at A (0, 6) = 6 x 0 + 12 x 16 = 72

Profit at B (18, 0) = 6 x 18 + 12 x 0 = 108

Hence, the solution is at B (18, 0)