Question

A manufacturer wants to maximize the profit of two products. Product X yields a profit of $ 2.50 per unit, and product Y yields a profit of $3.20 per unit. Market tests and available resources have indicated the following constraints: The combined production level should not exceed 1200 units per month. The demand for product Y is no more than half the demand for product X. The production level of product X is less than or equal to 600 units plus three times the production level of product Y.

Answer 1

MAXIMIZE: Z= 2.5 X1 + 3.2 X2 1 X1 + 1 X2 < 1200 -1 X1 + 2 X2 < 0 1 X1 -3 X2 < 600 X1, X2 > 0

1200 1100 1000 900 809 700 600 500 400 300 200 D 100 0 E 200 400 600 800 1000 1200 100 300 509 700 900 1100

Point X coordinate (Xi) Y coordinate (X2) Value of the objetive function (Z) 0 0 o А 0 1200 3840 B 1200 0 3000 С 800 400 3280 D 1050 150 3105 E 600 0 1500

Number of X products= 800, Number of Y products=400

Maximum profit = 3280.