# Simplex method

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A nutritionalist is preparing a supplement mixture to add to a preparation of oatmeal. The nutritionalist has 3 mixtures available that can be combined to give the desired mixture. Each gram of the first mixture contains 1 unit of calcium, 1 unit of iron, and cost 70 cents. Each gram of the second mixture contains 1 unit of calcium, 2 units of iron, and costs 80 cents. Each gram of the third mixture contains 3 units of calcium, 1 unit of iron, and cost $1.40. Each batch of the product needs 35 units of calcium and 20 units of iron. How much of each mixture should be added to each batch of the product to meet these requirements at minimum cost?

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##### Solution Summary

This solution shows how to use the simplex method to solve a mixture problem regarding nutrition.

##### Solution Preview

Let three mixtures be added as X, Y and Z gm respectively.

Calcium:

1*X + 1*Y + 3*Z = 35

=> X + Y + 3Z = 35 ....(1)

Iron:

1*X + 2*Y + 1*Z = 20

=> X + 2Y + Z = 20 ...(2)

Cost:

C(X,Y,Z) = 70*X + 80*Y + ...

###### Education

- BEng, Allahabad University, India
- MSc , Pune University, India
- PhD (IP), Pune University, India

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