Formulate the above into a Linear Programming problem and
A cafeteria at one of the Universities has one special dish it serves like clockwork every Thursday at noon. This supposedly tasty dish is a casserole that contains sauted 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 resultantly eat the casserole, however, because the 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 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 for the casserole, she can signicantly reduce overall cafeteria operating costs. Invest time in determining how to minimize the costs of the casserole while maintaining nutritional and taste requirements. Maria 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 ofthe dish. Maria buys the potatoes and green beans from a wholesaler each week. Potatoes cost $0.40 per pound {lb} and green beans costs $1.00 per pound (lb) The student of the University has established nutritional requirements that each main dish of the cafeteria must meet. Specically, the dish must contain 180 grams of protein, 80 mg of iron, and 1050 mg of Vitamin C. (There are 454 grams in one lb and 1000 mg in one gram}. For simplicity when planning, Maria assumes that only the potatoes and green beans contribute to the nutritional content ofthe casserole. Because Maria works at a cutting-edge technological University, she has been exposed to the numerous resources on the World Wide Web. She decides to surf the Web to nd the nutritional content of potatoes and green beans. Her research yields the following nutritional information about the two ingredients: Potatoes Green beans Protein 1.5 g per 100 g 5.67 g per 10 ounces Iron 0.3 mg per 100 g 3.402 mg per 10 ounce Vitamin C 12mg per 100 g 28.35 mg per 10 ounces {there are 28.35 g in one ounce.) Edson Branner, the cafeteria cook who is surprisingly concerned about taste, informs Maria that an edible casserole must contain at least a six-to-ve ratio in the weight of potatoes to green beans. Given the number of students who eat in then the cafeteria, Maria knows that she must purchase enough potatoes and green beans to prepare a minimum of 10 kg of casserole each week. Again for simplicity in planning, she assumes that only the potatoes and green beans determine the amount of casserole that can be prepared. 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
