Answer :

Let required production of product A and B be x and y respectively

Given, profits on one unit of product A and B are Rs 2 and Rs 3 respectively, so profits on x units of product A and y units of product B are given by 2x and 3y respectively. Let Z be total profit, so

Z = 2x + 3y

Given, production of 1 unit of product A and B require 1 hour and 2 hours of grinding respectively, so, production of x units of product A and y units of product B require x hours and 2y hours of grinding respectively but the maximum time available for grinding is 3 hours, so

x + 2y ≤ 30 (First constraint)

Given, production of 1 unit of product A and B require 3 hours and 1 hours of turning respectively, so x units of product A and y units of product B require 3x hours and y hours of turning respectively but total time available for turning is 60 hours, so

3x + y ≤ 60 (Second constraint)

Given, production of 1 unit of product A and B require 6 hour and 3 hours of assembling respectively, so production of x units of product A and y units of product B require 6x hours and 3y hours of assembling respectively but total time available for assembling is 200 hours, so

6x + 3y ≤ 200 (Third constraint)

Given, production of 1 unit of product A and B require 5 hours and 4 hours of testing respectively, so production of x units of product A and y units of product B require 5x hours and 4y hours of testing respectively but total time available for testing is 200 hours, so

5x + 4y ≤ 200 (Fourth constraint)

Hence, mathematical formulation of LPP is,

Find x and y which

maximize Z = 2x + 3y

Subject to constraints,

x + 2y ≤ 30

3x + y ≤ 60

6x + 3y ≤ 200

5x + 4y ≤ 200

and, x, y ≥ 0 [Since production cannot be negative]

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