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Question

A sweet-shop makes gift packet of sweets by combining two special types of sweets A and B which weigh 7 kg. Atleast 3 kg of A and no more than 5 kg of B should be used. The shop makes a profit of Rs. 15 on A and Rs. 20 on B per kg. Determine the product mix so as to obtain maximum profit.

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Solution

Solution:
Let amount of A type of sweets =x kg
Let amount of B type of sweets =y kg
x0,y0 (I)
In one gift packet both types of sweets are to be included but not more than 7 kg.
x+y7 (II)
A type of sweets must be at least 3 kg.
x3 (III)
B type of sweets no more than 5 kg.
y5 (IV)
Profit Rs. 15 on A and Rs. 20 on B per kg.
Profit function f=15x+20y
The corner points for the graph are (3,4),(3,0) and (7,0)
x yf=15x+20y
34 125
3 0 45
7 0105
Maximum Profit of Rs. 125 can be gained when the mixture contains 3 kg of A and 4 kg of B.

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