Question

A diet is to contain at least 4000 units of carbohydrates, 500 units of fat and 300 units of protein. Two foods a and b are available. Food a costs 2 dollars per unit and food b costs 4 dollars per unit. A unit of food a contains 10 units of carbohydrates, 20 units of fat and 15 units of protein. A unit of food b contains 25 units of carbohydrates, 10 units of fat and 20 units of protein. Formulate the problem as an lpp so as to find the minimum cost for a diet that consists of a mixture of these two foods and also meets the minimum requirements.

Answer 1

Explanation:

let x carbohydrate

y fat

z protein

a denotes food A b denotes food B

ma+nb=minimum requirement

m(10x+20y+15z)+n(25x+10y+20z)=4000x+500y+300z

equating x,y,z

10m+25n=4000

20m+10n=500

15m+20n=300

solving we get,

40m+20n-15m-20n=1000-300

25m=700

m=28

Answer 2

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