Question

A manufacturing concern manufactures two products A and B. The products go through three processes: processing, fabrication and assembly. The manufacturing time per unit required to make them, the profit per unit, and the capacity available at each work center are as follows :

WORK CENTER (IN HOURS)

product Machining frabication assembly profit per unit

A 1 5 3 80

B 2 4 1 100

total capacity 720 1800 900

A) Formulate the above information to optimize the profit of the manufacturing concern

B) Find graphical solution.

Answer 1

A)

x is the number of products A, y is the number of products B

$x+2y\leq720$

$5x+4y\leq1800$

$3x+y\leq900$

$x\geq0,y\geq0$

Objective: $80x+100y\to$ max

B)

Maximum of objective function (profit) is at point $(120,300)$ :

$80\cdot120+100\cdot300=39600$