Question

A company manufactures two products X and Y. Each product has to be processed in three departments: welding, assembly and painting. Each unit of X spends 2 hours in the welding department, 3 hours in assembly and 1 hour in painting. The corresponding times for a unit of Y are 3, 2 and 1 respectively. The man-hours available in a month are 1500 for the welding department, 1500 in assembly and 550 in painting. The contribution to profits are $100 for product X and $120 for product Y.

Formulate the appropriate linear programming problem

Solve it graphically to obtain the optimal solution for the maximum contribution

Answer 1

Solution:

Product       Welding     Assembly   Painting     =   Cont. to profit

X               2x hours      3x hours     1xhour    =    $100x

Y               3y hours      2y hours     1y hour    =   $120y

                                                

Total hours     1500 hours    1500 hours  550 hours

available

Let X represent product X

Let Y represent Product Y

2x$+$3y = 1500

x $+$ y = 550

y= 550$-$ x

2x $+$ 3(550$-$ x) = 1500

2x $+$ 1650$-$ 3x = 1500

150 = x

y = 550$-$ 150

y = 400

Objective Function Z = 100x $+$ 120y

Z = 100(150) $+$ 120( 400)

Z = 15000+48000

Z = $63000