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. 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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