Q29 of 29 Page 1

A company produces two types of goods, A and B, that require gold and silver. Each unit of type A requires 3 g of silver and 1 g of gold while that of B requires 1 g of silver and 2 g of gold. The company can use at most 9 g of silver and 8 g of gold. If each unit of type A brings a profit of Rs40 and that of type B Rs50, find the number of units of each type that the company should produce to maximize the profit. Formulate and solve graphically the LPP and find the maximum profit.

Let number of units of type A be x and that of type B be y


LPP is Maximize P = 40x + 50y


subject to constraints


3x + y ≤ 9


x + 2y ≤ 8


x, y ≥ 0



P (3, 0) = 120


P (2, 3) = 230


P (0, 4) = 200


∴ Max profit = Rs230 at (2, 3)


So, to maximise profit, number of units of A = 2 and number of units of B = 3


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