Question

Every gram of wheat provides 0.1 gm of proteins and 0.25 gm of carbohydrates. the corresponding values for rice are 0.05 gm and 0.5 gm respectively. wheat costs rs. 4 per kg and rice rs. 6 per kg. the minimum daily requirements of proteins and carbohydrates for an average child are 50 gms and 200 gms respectively. in what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of proteins and carbohydrates at minimum cost. frame an l.p.p. and solve it graphically.

Answer 1

Answer:

Suppose x gms of wheat and y grams of rice are mixed in the daily diet. Since every gram of wheat provides 0.1 gm of proteins and every gram of rice gives 0.05 gm of proteins. Therefore, x gms of wheat and y grams of rice will provide 0.1x + 0.05y gms of proteins.

But the minimum daily requirement of proteins is of 50 gms

∴ 1.0 x + 05.0 y ≥ 50 ⇒ 50 10 20 + ≥ x y

400 g of wheatIS REQUIRED

Similarly, x gms of wheat and y gms of rice will provide 25.0 x + 5.0 y gms of carbohydrates and the minimum daily requirement of carbohydrates is of 200 gms

minimum cost is Rs 2.80

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