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.