A cafeteria at All-State University has one special dish it serves like clockwork every Thursday at noon. This supposedly tasty dish is a casserole that contains saut©ed 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 cafeteria provides only a limited selection of dishes for Thursdays lunch (namely, the casserole).
Maria Gonzalez, the cafeteria 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 cafeteria menu, she concludes that if she can cut costs on the ingredients purchased fo
...r the casserole, she can significantly reduce overall cafeteria operating costs. She therefore decides to invest time in determining how to minimize the costs of the casserole while maintaining nutritional and taste requirements.
Maria 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 Maria should purchase each week for the casserole to minimize the ingredient costs while meeting nutritional, taste, and demand requirements. Before she makes her final decision, Maria plans to explore the following questions independently except where otherwise indicated. ) Maria is not very concerned about the taste of the casserole; she is only concerned about meeting nutritional requirements an
cutting costs. She therefore forces Edson to change the recipe to allow for only at least a one to two ratio in the weight of potatoes to green beans. Given the new recipe, determine the amount of potatoes and green beans Maria should purchase each week. (c) Maria decides to lower the iron requirement to 65 mg since she determines that the other ingredients, such as the onions and cream of mushroom soup, also provide iron.
Determine the mount of potatoes and green beans Maria should purchase each week given this new iron requirement. (d) Maria learns that the wholesaler has a surplus of green beans and is therefore selling the green beans for a lower price of $0. 50 per lb. Using the same iron requirement from part (c) and the new price of green beans, determine the amount of potatoes and green beans Maria should purchase each week. (e) Maria decides that she wants to purchase lima beans instead of green beans since lima beans are less expensive and provide a greater amount of protein and iron than green beans.
Maria again wields her absolute power and forces Edson to change the recipe to include lima beans instead of green beans. Maria knows she can purchase lima beans for $0. 60 per lb from the wholesaler. She also knows that lima beans contain 22. 68 gof protein per 10 ounces of lima beans, 6. 804 mg of iron per 10 ounces of lima beans, and no vitamin C. Using the new cost and nutritional content of lima beans, determine the amount of potatoes and lima beans Maria should purchase each week to minimize
the ingredient costs while meeting nutritional, taste, and demand requirements.
The nutritional requirements include he reduced iron requirement from part (c). (f) Will Edson be happy with the solution in part (e)? Why or why not? (g) An All-State student task force meets during Body Awareness Week and determines that All-State Universitys nutritional requirements for iron are too lax and that those for vitamin C are too stringent. The task force urges least 120 mg of iron and at least 500 mg of vitamin C. Using potatoes and lima beans as the ingredients for the dish and using the new nutritional requirements, determine the amount of potatoes and lima beans Maria should purchase each week.
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