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# CMU ISM 95760 - Fast Food Case: Wendy’s

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Fast Food Case: Wendy’sOne of the oldest applications of linear programming was to the “diet problem”. The original incarnation had significant policy relevance (setting welfare payments basedon estimates of the minimum cost way of eating a nutritionally balanced diet). A much smaller scale but more personal application is trying to figure out what to order at a fast food restaurant such as Wendy’s.Price and nutritional data for some common Wendy’s menu items are given below. The FDA suggests that a typical male should consume at least 2400 calories and 60 grams of protein per day, get 100% of certain vitamins, while consuming no more than80 grams of fat, 3000 milligrams of sodium, 300 milligrams of cholesterol, or 300 grams of carbohydrates. Recommendations for females are similar except only 1800 calories are needed and daily consumption of fat should not exceed 60 grams.a) Find the lowest cost meal at Wendy’s that meets RDA for calories, protein, fat, sodium,cholesterol, and carbohydrates for an average female allowing for fractional orders (e.g., 0.657 servings of chicken nuggets). I.e., don’t worry about vitamins and minerals yet. Note: Some RDA are maximums; some are minimums.b) Repeat part (a) but ordering only whole multiples of any item.c) How much more would the meal cost if one insisted on meeting the RDA for Vitamins A and C, calcium, and iron (fractional orders allowed again).d) Suppose one also insisted on having a Double Stack? Or a Baconator?e) Repeat parts (a) and (c) but using the RDA requirements for males.f) Suppose a female wants to minimize fat while staying within a budget and meeting RDA requirements cholesterol, sodium, carbs, protein, and calcium (but not the vitamins or iron). Plot the amount of fat in her meal as a function of her budget, for budgets varying from \$6 to \$10.00 in \$0.25 increments. (Fractional orders are allowed.)Note what this plot says about both the ability of wealthy people to remain healthy and the presence of diminishing returns to increasing

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