A Dietician Wants to Formulate a Low Cost, High Calorie

A dietician wants to formulate a low cost, high calorie food product for a customer. The following information is available about the 2 ingredients which can be combined to make the food. The customer wants 1000 pounds of the food product and it should contain 250 pounds of Food 1 and 300 pounds of Food 2. The final cost of the blend should be about $1.15 and contain about 2500 calories per pound. The percent of fat, protein, carbohydrate in each food is summarized below with the target values for the goals. The dietician would prefer the food product be low in fat while also high in protein and carbohydrates.
$\begin{array}{lccc}& \text { Food 1}&\text { Food 2}& \text { TARGET}\\ \hline \text { Cost }(\$ / \text { pound) } & \$ 1.00 & \$ 1.25 & \$ 1.15 \\\text { Fat } & 15 \% & 25 \% & 300 \text { pounds } \\\text { Protein } & 35 \% & 40 \% & 370 \text { pounds } \\\text { Carbohydrate } & 50 \% & 35 \% & 400 \text { pounds } \\\text { Calories/pound } & 3000 & 2000 & 2500 \\\text { Pounds of food 1 } & & & 250 \\\text { Pnunds of food2 } & & & 300\end{array}$

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