Case study: Reducing cafe costs

A cafe at the university has one special dish it serves like clockwork every Monday at noon. This supposedly tasty dish is a casserole that contains sautéed onions, boiled sliced potatoes, green beans, and cream of mushroom soup. Unfortunately, students fail to see the special quality of this dish, and they loathingly refer to it as the Killer Casserole. The students reluctantly eat the casserole, however, because the cafe provides only a limited selection of dishes for Monday's lunch (namely, the casserole).

Jane Lim, the cafe manager, is looking to cut costs for the coming year, and she believes that one sure way to cut costs is to buy less expensive and perhaps lower quality ingredients. Because the casserole is a weekly staple of the cafe menu, she concludes that if she can cut costs on the ingredients purchased for the casserole, she can significantly reduce overall cafe operating costs. She therefore decides to invest time in determining how to minimise the costs of the casserole while maintaining nutritional and taste requirements.

Jane focuses on reducing the costs of the two main ingredients in the casserole, the potatoes and green beans. These two ingredients are responsible for the greatest costs, nutritional content, and taste of the dish.

Jane buys the potatoes and green beans from a wholesaler each week. Potatoes cost $0.30 per pound (lb), and green beans cost $0.95 per lb.

The university has established nutritional requirements that each main dish of the cafe must meet. Specifically, the dish must contain 160 grams (g) of protein, 65 milligrams (mg) of iron, and 1,000 mg of vitamin C. For simplicity when planning, Jane assumes that only the potatoes and green beans contribute to the nutritional content of the casserole.

Because Jane works at a cutting-edge technological university, she has been exposed to the numerous resources on the Internet. She decides to find the nutritional content of potatoes and green beans. Her research yields the following nutritional information about the two ingredients.

(There are 28.35 g in one ounce, and 16 ounces in one pound)

Eddy Brooks, the cafe cook who is surprisingly concerned about taste, informs Jane that an edible casserole must contain at least a six-to-five ratio in the weight of potatoes to green beans.

Given the number of students who eat in the cafe, Jane knows that she must purchase enough potatoes and green beans to prepare a minimum of 12 kilograms (kg) of casserole each week. (There are 1,000 g in one kg.) Again, for simplicity in planning, she assumes that only the potatoes and green beans determine the amount of casserole that can be prepared. Jane does not establish an upper limit on the amount of casserole to prepare since she knows all leftovers can be served for many days thereafter or can be used creatively in preparing other dishes.

a. Determine the amount of potatoes and green beans Jane should purchase each week for the casserole to minimise the ingredient costs while meeting nutritional, taste, and demand requirements.

Before she makes her final decision, Jane plans to explore the following questions independently, except where otherwise indicated.

b. Student Union meets during Health Awareness Week and determines that The university's nutritional requirements for iron are too lax and that those for vitamin C are too stringent. The Union urges the university to adopt a policy that requires each serving of an entrée to contain at least 100 mg of iron and at least 500 mg of vitamin C. Using the new nutritional requirements, determine the amount of potatoes and green beans Jane should purchase each week.

c. Jane learns that the wholesaler has a shortage of green beans and is now selling the green beans for a higher price of $1.20 per lb. Using the new price of the green beans, determine the amount of potatoes and green beans Jane should purchase each week.

d. Using the new nutritional requirements in part b and the new price of green beans in part c, determine the amount of potatoes and green beans Jane should purchase each week.

e. Based on part d, which required nutrition would affect the cost if it were to be changed. Why?