4. You would like to make a nutritious meal of eggs, mixed vegetables and brown rice. The meal should provide at least 35 g of carbohydrates, at least 25 g of protein, and no more than 45 g of fat. One serving of eggs contains 2 g of carbohydrates, 18 g of protein, and 12 g of fat. A serving of mixed vegetables contains 14 g of carbohydrates, 15 g of protein, and 8 g of fat. A serving of rice contains 40 g of carbohydrates, 6 g of protein, and 1 g of fat. A serving of eggs costs $2, a serving of mixed vegetables costs $4, and a serving of rice costs $3. Formulate a linear optimization model that could be used to determine the number of servings of eggs, mixed vegetables, and rice for your meal that meets the nutrition requirements at minimal cost. (You do not need to find the optimal solution to the model you formulate.)

Question #5

The Sonoma Apple Products Company purchases apples from local growers and makes applesauce and apple juice. It costs $0.85 to produce a jar of applesauce and $0.75 to produce a bottle of apple juice. The company has a policy that at least 25 percent but no more than 65 percent of its output must be applesauce.

The company wants to meet but not exceed the demand for each product. The marketing manager estimates that the demand for applesauce is a maximum of 4500 jars, plus an additional 4 jars for each $1 spent on advertising for applesauce. The maximum demand for apple juice is estimated to be 3800 bottles, plus an additional 5 bottles for every $1 spent on advertising for apple juice. The company has $16,500 to spend on producing and advertising its two products. Applesauce sells for $2 per jar, and apple juice sells for $1.50 per bottle.

Formulate a linear optimization model to help the company determine how many units of each product to produce, and how much advertising to spend on each product, in order to maximize profit. (You do not need to find the optimal solution to the model you formulate.)