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Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60 / kg and Food Q costs Rs 80 / kg. Food P contains 3 units/kg

Text Solution

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Let `x` kg of first type of food and `y` kg of second type of food be mixed.

According to the problem,
Minimise `Z=60x+80y`
and constraints `xge0, yge0`
`3x+4yge8,5x+2yge11`
First, draw the graph of the lines `3x+4y=8` and `5x+2y=11`

Now find the feasible region from the constraints `3x+4yge8,5x+2yge11,xge0,yge0` and shade it. The vertices of this shaded region are `A(0,11/2),B(2,1/2)` and `C(8/3,0)`. We find the value of `Z` at these vertices.

Therefore, the minimum cost of the mixture is Rs. 160.
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