# Linear programming for optimization

2. Blending Problem (20%): Determine the optimal amounts of three ingredients to include in an animal feed mix. The final product must satisfy several nutrient requirements. The possible ingredients, the nutrient contents (as proportion of the ingredient), and the unit costs are shown in the table. The mixture must meet the following restrictions:

Calcium: at least 0.8% but not more than 1.2%

Protein: at least 22%

Fiber: at most 5%

The problem is to find the composition of the feed mix that satisfies these constraints while minimizing the cost.

Ingredient Calcium Protein Fiber Unit Cost (cents/kg)

Limestone 0.38 0.0 0.0 10.0

Corn 0.001 0.09 0.02 30.5

Soybean 0.002 0.50 0.08 90.0

Formulate this problem into a LP model.

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#### Solution Summary

The solution provides a step-by-step example of formulating a linear programming model for a mixture problem. See the attached files for details (MS Word and Excel). Tables are included in documents.