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# Simplex method

A baby products firm produces a strained baby food containing liver and milk, each of which contribute protein and iron to the baby food. Each jar of baby food must have 36 milligrams of protein and 50 milligrams of iron. The company has developed the following linear programming model to determine the number of ounces of liver (X1) and milk (X2) to include in each jar of baby food to meet the requirements for protein and iron at the minimum cost.

minimize Z = 0.05 X1 + 0.10 X2 (cost, \$)

subject to

6X1 + 2X2 > 36 (protein, mg)
5X1 + 5X2 > 50 (iron, mg,)
X1, X2 > 00

I must complete this model using the simplex method

#### Solution Preview

Solution.

Use Simplex Method, we get

Optimal Solution: Z = 0.5; x 1= 10, x2 = 0

Tableau #1
x1 x2 s1 s2 -Z
6 2 -1 0 0 36
5 5 0 -1 0 50
0.05 0.1 0 ...

#### Solution Summary

This provides an example of solving a linear programming problem with the simplex method. Minimizing functions are analyzed.

\$2.19