Given the number of students who eat in the cafeteria, Maria knows that she must purchase enoughpotatoes and green beans to prepare a minimum of 10 kilograms (kg) of casserole each week. (There are1,000 g in one kg.) Again, fur simplicity in planning, slhe assumes that uıly the potatoes and green beansdetermine the amount of casserole that can be prepared. Maria does not establish an upper limit on theamount of casserole to prepare since she knows all leftovers can be served for many days thereafter or canbe used creatively in preparing other dishes.a. Determine the amount of potatoes and green beans Maria should purchase each week for thecasserole to minimize the ingredient costs while meeting nutritional, taste, and demandrequirements. Before she makes her final decision, Maria plans to explore the followingquestions independently, except where otherwise indicated.b. Maria is not very concerned about the taste of the casserole; she is only concerned about meetingnutritional requirements and cutting costs. She therefore forces Edson to change the recipeto allow only for at least a one-to-two ratio in the weight of potatoes to green beans. Giventhe new recipe, determine the amount of potatoes and green beans Maria should purchaseeach week.c. Maria decides to lower the iron requirement to 65 mg since she determines that the otheringredients, such as the onions and cream of mushroom soup, also prowide iron. Determinethe amount of potatoes and green beans Maria should purchase each week given this newiron requirement.d. Maria learns that the wholesaler has a surplus of green beans and is therefore selling the greenbeans for a lower price of $0.50 per Ib. Using the same iron requirement from part c and thenew price of green beans, determine the amount of potatoes and green beans Maria shouldpurchase each week.e. Maria decides that she wants to purchase lima beans instead of green beans since lima beans areless expensive and provide a greater amount of protein and iron than green beans. Mariaagain wields her absolute power and forces Edson to change the recipe to include limabeans instead of green beans. Maria knows she can purchase lima beans for $0.60 per Ibfrom the wholesaler. She also knows that lima beans contain 22.68 g of protein and 6.804mg of iron per 10 ounces of lima beans and no vitamin C. Using the new cost and nutritionalcontent of lima beans, determine the amount of potatoes and lima beans Maria shouldpurchase each week to minimize the ingredient costs while meeting nutritional, taste, anddemand requirements. The nutritional requirements include the reduced iron requirementfrom part c.f. Will Edson be happy with the solution in part e? Whywhy not?g. An All-State student task force meets during Body Aware ness Week and determines that All-State University's nutritional requirements for iron are too lax and that those for vitamin Care too stringent. The task force urges the university to adopt a policy that requires eachserving of an entrée to contain at 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 nutritionalrequirements, deter mine the amount of potatoes and lima beans Maria should purchaseeach week. Cutting Cafeteria CostsA cafeteria at All-State University has one special dish it serves like clockwork every Thursday at noon. Thissupposedly tasty dish is a casserole that contains sautéed onions, boiled sliced potatoes, green beans, andcream of mushroom soup. Unfortunately, students fail to see the special quality of this dish, and theyloathingly refer to it as the Killer Casserole. The students reluctantly eat the casserole, however, becausethe cafeteria provides only a limited selection of dishes for Thursday's lunch (namely, the casserole).Maria Gonzalez, the cafeteria manager, is looking to cut costs for the coming year, and she believes that onesure way to cut costs is to buy less expensive and perhaps lower quality ingredients. Because the casseroleIs a weekly staple of the cafeteria menu, she concludes that if she can cut costs on the ingredientspurchased for the casserole, she can significantly reduce overall cafeteria operating costs. She thereforedecides to invest time in determining how to minimize the costs of the casserole while maintainingnutritional and taste requirements.Maria focuses on reducing the costs of the two main ingredients in the casserole, the potatoes and greenbeans. These two ingredients are responsible for the greatest costs, nutritional content, and taste of thedish.Maria buys the potatoes and green beans from a wholesaler each week. Potatoes cost $0.40 per pound (Ib).and green beans cost $1.00 per Ib.All-State University has established nutritional requirements that each main dish of the cafeteria mustmeet. Specifically, the dish must contain 180 grams (g) of protein, 80 milligrams (mg) of iron, and 1,050 mgof vitamin C. (There are 454 g in one Ib and 1,000 mg in one g) For simplicity when planning, Mariaassumes that only the potatoes and green beans contribute to the nutritional content of the casserole.Because Maria works at a cutting-edge technological university, she has been exposed to the numerousresources on the World Wide Web. She decides to surf the Web to find the nutritional content of potatoesand green beans. Her research yields the following nutritional information about the two ingredients.PotatoesGreen Beans15 g per 100 g0.3 mg per 100 g12 mg per 100 gProtein5.67 g per 10 ounces3.402 mg per 10 ounces28.35 mg per 10 ouncesIronVitamin C(There are 28.35 g in one ounce.)Edson Branner, the cafeteria cook who is surprisingly concerned about taste, informs Maria that an ediblecasserole must contain at least a six-to-five ratio in the weight of potatoes to green beans.

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