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  • 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 atmost 9 g of silver and 8 g of gold. I

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 atmost 9 g of silver and 8 g of gold. If each unit of type A brings a profit of Rs 40 and that of type B Rs 50, 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.

 

 

 

 
 
 
 
 

Answers (1)

Lets x and y number of units of type A and B goods are produced To maximize : Z= 40x+50y \,\; in \; Rs subject to constraints : x\geq 0\; y\geq 0
3x+y\leq 9\; ,x+2y\leq 8
Corner points                                           value of Z(in Rs)
O(0,0)                                                            0
A(3,0)                                                           120
B(2,3)                                                            230 \leftarrow Maximum
C(0,4)                                                           200
so maximum profit of 230 Rs is obtained when 2 & 3 units of Type A and Type B goods are made, resp.

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Ravindra Pindel

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