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Linear Programming : Formulating Equations and Minimizing Cost

A biologist must make a nutrient for her algae. The nutrient must contain three basic elements D, E, F, and must contain at least 10kg of D, 12kg of E, and 20Kg of F. The nutrient is made from three ingredients, I, II, III. The quantity of D, E, F in one unit of each of the ingredients is given in the following chart.

Ingredient I II III
Kilograms of Elements(per unit of ingredient) D 4 1 10
E 3 2 1
F 0 4 5
Cost per unit(in $) 4 7 5

Using simplex method, define variables, find how many units of each ingredient are required to meet the biologists need at minimum cost?

How do I set up the equations for this problem?

Solution Summary

The simplex method is fully explained for a LP problem. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.