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in Linear Programming by (25.7k points)
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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.

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Let the firm manufacture x number of A and y number of B products.

∴According to the question,

X + y ≤ 300, 2x + y ≤ 360, x ≥ 0, y ≥ 0

Maximize Z = 5x + 3y

The feasible region determined X + y ≤ 300, 2x + y ≤ 360, x ≥ 0, y ≥ 0 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

Corner Point Z = 5x + 3y
A(0, 0) 0
B(0, 300) 900
C(60, 240) 1020 Maximum
D(180, 0) 900

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

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

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