Q. 6

A company sells two different products A and B. The two products are produced in a common production process and are sold in two different markets. The production process has a total capacity of 45000 man - hours. It takes 5 hours to produce a unit of A and B hours to produce a unit of B. The market has been surveyed and company officials feel that the maximum number of units of A that can be sold is 7000 and that of B is 10, 000. If the profit is Rs 60 per unit for the product A and Rs 40 per unit for the product B, how many units of each product should be sold to maximize profit? Formulate the problem as LPP.

Answer :


Let required production of product A be x units and production of product B be y units.


Given, profits on one unit of product A and B are Rs 60 and Rs 40 respectively, so profits on x units of product A and y units of product B are Rs 60x and Rs 40y.


Let Z be the total profit, so
Z = 60x + 40y


Given, production of one unit of product A and B require 5 hours and 3 hours respectively man hours, so x unit of product A and y units of product B require 5x hours and 3y hours of man hours respectively but total man hours available are 45000 hours, so


5x + 3y 45000 (First constraint)


Given, demand for product A is maximum 7000, so


x 7000 (Second constraint)


Hence, mathematical formulation of LPP:


Find x and y which


maximize Z = 60x + 40y


Subject to constraints,


5x + 3y 45000


x 7000


y 10000


x, y 0 [Since production cannot be less than zero]


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