Read and understand the following diet optimization case. Formulate the problem with a linear programing model $($determine the decision variables, write down the objective function, and specify the constraints in the Excel file, $1\mathrm{.}5$pts$).$ Use Excel solver to solve the case $($highlight the optimal solution and objective value, $1\mathrm{.}5$pts$).$ Submit the resulting Excel file.

Diet Optimization:

A nutritionist wants to create a balanced diet plan for a client using three types of food: apples, bananas, and carrots. Each food item has specific nutritional values per unit as follows:

Apples provide $2$ grams of protein, $3$ grams of carbohydrates, and $1$ gram of fat.

Bananas provide $1$ gram of protein, $2$ grams of carbohydrates, and $0\mathrm{.}5$ grams of fat.

Carrots provide $1\mathrm{.}5$ grams of protein, $1$ gram of carbohydrates, and $0\mathrm{.}2$ grams of fat.

The nutritionist wants to determine the number of units of each food item to include in the diet plan while meeting the client's daily nutritional requirements of at least $50$ grams of protein, $60$ grams of carbohydrates, and $15$ grams of fat, while minimizing the cost. The cost per unit for each food item is $$0\mathrm{.}50$ for apples, $$0\mathrm{.}40$ for bananas, and $$0\mathrm{.}30$ for carrots.

Drag a file here, or click to select a file to upload

Drag a file here, or

Choose a file to upload

No file chosen

or