An All-State University cafeteria has a special dish that serves like clockwork every Thursday at noon. This supposedly savory dish is a casserole containing sautéed onions, sliced boiled potatoes, green beans, and cream of mushroom soup. Unfortunately, students do not see the special quality of this dish, and dismissively refer to it as Killer Casserole. However, the students reluctantly eat the casserole because the cafeteria offers only a limited selection of dishes for Thursday lunch (namely the casserole).

María González, the cafeteria manager, is looking to reduce costs for the coming year and believes that a sure way to reduce costs is to buy less expensive and perhaps lower-quality ingredients. Because the casserole is a weekly staple of the cafeteria menu, she concludes that if she can reduce the costs of the ingredients she buys for the casserole, she can significantly reduce the cafeteria's overall operating costs. She, therefore, decides to invest time in determining how to minimize casserole costs while maintaining nutritional and flavor requirements.

Maria focuses on reducing the costs of the two main ingredients in the casserole, the potatoes, and the green beans. These two ingredients are responsible for the higher costs, nutritional content, and flavor of the dish.
Maria buys potatoes and green beans from a wholesaler every week. Potatoes cost $0.40 per pound and green beans cost $1.00 per pound.

All-State University has established nutritional requirements that each cafeteria entrée must meet. Specifically, the total amount of dish prepared for all students for one meal must contain 180 grams (g) of protein, 80 milligrams (mg) of iron, and 1,050 mg of vitamin C. (There are 453.6 g in 1 lb and 1,000 mg in 1 g.) To simplify planning, Maria assumes that only the potatoes and green beans contribute to the nutritional content of the casserole.

Because Maria works at a state-of-the-art technological university, she has been exposed to numerous resources on the World Wide Web. She decides to go online to find the nutritional content of potatoes and green beans. Her research yields the following nutritional information on the two ingredients:

Protein Potatoes: 1.5 g per 100 g Green beans: 5.67 g per 10 ounces

Iron 0.3 mg per 100 g 3.402 mg per 10 units

Vitamina C 12mg por 100g 28,35 mg por 10ou

Edson Branner, the cafeteria cook who is surprisingly concerned with flavor, informs Maria that an edible casserole should contain at least a six to five ratio by weight of potatoes to green beans.
Given the number of students eating in the cafeteria, Maria knows that she must buy enough potatoes and green beans to prepare a minimum of 10 kilograms (kg) of stew each week. (There is

1,000 g in 1 kg.) Again to simplify planning, assume that only the potatoes and green beans determine the amount of stew that can be made. Maria does not set an upper limit on the amount of casserole to prepare, as she knows that all leftovers can be served for many days or used creatively in the preparation of other dishes.

(a) Determine the number of potatoes and green beans Maria should buy each week for the casserole to minimize ingredient costs and meet nutritional, taste, and demand requirements.
Before making her final decision, Maria plans to explore the following questions independently, except where otherwise noted.

In this problem, "Reduce Cafeteria Cost," how was the amount determined?

Answer rating: 100% (QA)

The goal in the Reduce Cafeteria Cost problem is to minimize the cost of the casserole ingredients p... View the full answer