Q. 265.0( 2 Votes )

A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of the first machine is 12 hours and that of the second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines, and each unit of product B requires 2 hours on the first machine and 1 hour on the second machine. Each unit of product A is sold at ` 7 profit and that of B at a profit of ` 4. Find the production level per day for maximum profit graphically.

Answer :

Given: A manufacturer produces two products A and B


To find: the production level of A and B per day for maximum profit graphically


Let the number of units of products A and B to be produced each day be x and y respectively



Let z be a total profit of manufacture


Each unit of product A is sold at Rs. 7 profit and that of B at a profit of Rs. 4


z = 7x + 4y


We need to maximize the cost


Hence, the mathematical formulation of LPP is


Maximize z = 7x + 4y


subject to the constraints,


3x + 2y 12


3x + y 9


x, y 0


The feasible region determined by the system of constraints is as follows:



The corner points of the enclosed region are A(0, 6) , B(2, 3), C(3, 0)


The value of z at these corners points is as follows:


Case 1: A(0, 6)


z = 7x + 4y


z = 7(0) + 4(6)


z = 0 + 24


z = 24


Case 2: B(2, 3)


z = 7x + 4y


z = 7(2) + 4(3)


z = 14 + 12


z = 26


Case 3: C(3, 0)


z = 7x + 4y


z = 7(3) + 4(0)


z = 21 + 0


z = 21


The value of z is maximum in the second case at point B(2, 3)


Hence, the unit of products A and B to be produced are 2 and 3 respectively, and the total maximum profit is Rs. 26


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