The trainer for a local football team has been asked to develop a nutritional supplement for the team to meet specific dietary requirements. No product currently on the market meets all of the specifications set out by the coaches so the trainer will have to come up with a mix of four commercial products: Muscle Tone, High Build, TrainR, and Biggie Food. These products have the following nutrients in grams per pound of product:
Product Carbohydrates Protein Calcium Salt Cost
Muscle Tone 75 55 120 1 $2.20/lb
High Build 15 65 65 2 1.60/lb
Train R 35 50 80 3 0.60/lb
Biggie Food 35 30 95 3 0.50/lb
The coaches want no more than 50 grams per pound to be carbohydrates, and no more than 1.5 grams per pound to be salt. There should be at least 50 grams per pound of protein and at least 90 grams per pound of calcium. From this information, formulate a cost minimizing linear model.