Chapter 3, Problem 18QP

Tuckered Outfitters plans to market a custom brand of packaged trail mix. The ingredients for the trail mix will include Raisins, Grain, Chocolate Chips, Peanuts, and Almonds costing, respectively, $2.50, $1.50, $2.00, $3.50, and $3.00 per pound. The vitamin, mineral, and protein content of each of the ingredients (in grams per pound) is summarized in the following table along with the calories per pound of ingredient:

The company would like to identify the least costly mix of these ingredients that provides at least 40 grams of vitamins, 15 grams of minerals, 10 grams of protein, and 600 calories per two pound package. Additionally, they want each ingredient to account for at least 5% and no more than 50% of the weight of the package.

1. a. Formulate a LP model for this problem.
2. b. Implement your model in a spreadsheet and solve it.
3. c. What is the optimal mix and how much is the total ingredient cost per package?