A company produces two types of goods, A and B, that require gold and silver. Each unit of type A requires 3g of silver and 1g of gold while that of type B requires 1g of silver and 2g of gold. The company can use at the most 9g of silver and 8g 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 profit. Formulate the above LPP and solve it graphically and also 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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