Question: The cafeteria of a school has one special dish it serves every Tuesday at lunch. The tasty dish is a casserole that contains sautéed onions, boiled sliced potatoes, green beans, and cream of mushroom soup. The students don’t seem to like it too much and refer to it as the Killer Casserole. The students eat it, nonetheless, because of the limited selection available. The cafeteria manager, Ted, is looking to cut costs for the coming year. He believes that one sure way to cut costs is to buy less expensive ingredients. Since the casserole is a weekly staple of the cafeteria menu, he concludes that he could significantly reduce operating costs by cutting the costs on the ingredients purchased for the casserole. Thus, Ted decides to invest some time to determine how to minimize the costs of the casserole while maintaining nutritional and taste requirements. Ted focuses on reducing the costs of the two main ingredients in the casserole, the potatoes and the green beans. Ted buys the potatoes and green beans from a wholesaler each week. Potatoes cost $0.49 per pound, and green beans cost $1.99 per pound. The school has established nutritional requirements that each main dish of the cafeteria must meet. Specifically, the total amount of the dish prepare for all students for one meal must contain 180g (grams) of protein, 80mg (milligrams) of iron, and 1,050 mg of vitamin C. Note that there are 453g in 1 lb. To simplify the problem Ted assumes that only potatoes and green beans contribute to the nutritional content of the casserole. The following table contains the nutritional contents of each food.

The cafeteria cook, who is very concerned about taste, tells Ted 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 cafeteria, Ted knows that he must purchase enough potatoes and green beans to prepare a minimum of 10 kilograms (kg) of casserole each week. There are 1000g in 1 kg). Ted does not establish an upper bound on the amount of casserole to prepare since he knows all leftovers can be served for many days thereafter or can be used creatively in preparing other dishes. Determine the amount of potatoes and green beans Ted should purchase each week for the casserole to minimize the ingredient costs while meeting the nutritional, taste and demand requirements.