# 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.[CBSE 2018]

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 maximize profit, number of units of A = 2 and number of units of B = 3

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