A firm manufactures two types of product, A and B, and sells them at a profit of ₹5 per unit of type A and ₹3 per unit of type B. Each product is processed on two machines, M1 and M2 . one unit of type A requires one minute of processing time on M1 and two minutes of processing time on M2; whereas one unit of type B requires one minute of processing time on M1 and one minute on M2. Machines M1 and M2 are respectively available for at most 5 hours and 6 hours in a day. Find out how many units of each type of product the firm should produce a day in order to maximize the profit. Solve the problem graphically.


Let the firm manufacture x number of Aand y number of B products.


According to the question,


X + y


Maximize Z = 5x + 3y


The feasible region determined X + y is given by



The corner points of feasible region are A(0,0) , B(0,300) , C(60,240) , D(180,0).The value of Z at corner point is



The maximum value of Z is 1020 and occurs at point (60,240).


The firm should produce 60 Aproducts and 240 B products to earn maximum profit of Rs.1020.


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