Q10 of 118 Page 31

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 ₹ 60 kg and Food Q costs ₹ 80 kg. Food P contains 3 units / kg of Vitamin A and 5 units / kg of Vitamin B while food Q contains 4 units / kg of Vitamin A and 2 units / kg of vitamin B. Determine the minimum cost of the mixture.

The above information can be expressed in the form of the following table:



Let the mixture contain ‘x’ kgs and ‘y’ kgs of food P and Q respectively.


Cost of food P = 60x


Cost of food Q = 80y


Cost of mixture = 60x + 80y


Now,


⟹ 3x + 4y ≥ 8


i.e. the minimum requirement of vitamin A from the mixture of P and Q is 8units, each of which contains 3units and 4units respectively.


⟹ 5x + 2y ≥ 11


i.e. the minimum requirement of vitamin B from the mixture of P and Q is 11 units, each of which contains 5units and 2units respectively.


Hence, mathematical formulation of the LPP is as follows:



The feasible region is Unbounded.


The corner points of the feasible region are as follows:



Z is minimised on the line joining points B(2,0.5) and .


The minimum cost of mixture is ₹160


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