Q4 of 118 Page 30

A firm manufactures two types of products A and B and sells them at a profit of Rs 2 on type A and Rs 3 on type B. Each product is processed on two machines M1 and M2. Type A requires one minute of processing time on M1 and two minutes of M2; type B requires one minute on M1 and one minute on M2. The machine M1 is available for not more than 6 hours 40 minutes while machine M2 is available for 10 hours during any working day. Formulate the problem as a LPP.

Given equation can be written in tabular form as



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


Given, profit 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 will be Rs 2x and Rs 3y respectively.


Let total profit be Z, so Z = 2x + 3y


Given, production of one unit of product A and B require 1 and 1 minute on machine M1 respectively, so production of x units of product A and y units of product B require x minutes and y minutes on machine M1 but total time available on machine M1 is 600 minutes, so


x + y ≤ 400 (First constraint)


Given, production of one unit of product A and B require 2 minutes and 1 minutes on machine M2 respectively. So, production of x units of product A and y units of product B require 2x minutes and y minutes respectively on machine M2, but machine M2 is available for 600 minutes, so


2x + y ≤ 600 (Second constraint)


Hence, the mathematical formulation of LPP is:


Find x and y which


maximize Z = 2x + 3y


Subject to constraints,


x + y ≤ 400


2x + y ≤ 600


and, x, y ≥ 0 [Since production of the product cannot be less than zero]


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2

A company is making two products A and B. The cost of producing one unit of products A and B are Rs 60 and Rs 80 respectively. As per the agreement, the company has to supply at least 200 units of product B to its regular customers. One unit of product A requires one machine hour whereas product B has machine hours available abundantly within the company. Total machine hours available for product A are 400 hours. One unit of each product A and B requires one labour hour each and total of 500 labour hours are available. The company wants to minimize the cost of production by satisfying the given requirements. Formulate the problem as a LPP.

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A firm manufactures 3 products A, B and C. The profits are Rs. 3, Rs. 2 and Rs. 4 respectively. The firm has 2 machines and below is the required processing time in minutes for each machine on each product.


Machines M1 and M2 have 2000 machine minutes respectively. The firm must manufacture 100 A’s, 200 B’s and 50 C’s but not more than 150 A’s. Set up a LPP to maximize the profit.

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A rubber company is engaged in producing three types of tyres A, B and C. Each type requires processing in two plants, Plant I and Plant II. The capacities of the two plants, in the number of tyres per day, are as follows:


The monthly demand for tyre A, B and C is 2500, 3000 and 7000 respectively. If plant I costs Rs 2500 per day, and plant II costs Rs 3500 per day to operate, how many days should each be run per month to minimize cost while meeting the demand? Formulate the problem as LPP.

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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.