The Food Services Department of a large university is concerned with the decision mak- ing related...

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The Food Services Department of a large university is concerned with the decision mak- ing related to the purchase of bread for use in the cafeterias of the university. The daily demand can be assumed to be uniformly distributed between 20 and 60 loaves. There are 20 slices in a loaf of bread and the selling price is $0.04 per slice. Any demand for bread when there is none on hand is lost but there is no associated loss of goodwill, etc. Any bread left over at the end of a day is used as ingredients for cooking (e.g., in bread pud- ding, stuffing, etc.). The value of such use is estimated to be $0.05 per loaf. The supplier, Easton Bakeries, in an effort to induce high consumption offers a discount structure as follows: Cost per loaf for first 50 loaves = $0.30 Cost per any loaf over 50 loaves = $0.20 The fixed cost of a procurement from the bakery = $5.00 a. Show the expected daily profit as a function of the number of loaves of bread ordered per day. b. What quantity of bread should be purchased per day? c. Outline how you would determine the daily loss in profit (compared with the optimal strategy) that would result if the university simply ordered the expected demand? d. What are some complexities that would have to be included to make the problem formulation more realistic? The Food Services Department of a large university is concerned with the decision mak- ing related to the purchase of bread for use in the cafeterias of the university. The daily demand can be assumed to be uniformly distributed between 20 and 60 loaves. There are 20 slices in a loaf of bread and the selling price is $0.04 per slice. Any demand for bread when there is none on hand is lost but there is no associated loss of goodwill, etc. Any bread left over at the end of a day is used as ingredients for cooking (e.g., in bread pud- ding, stuffing, etc.). The value of such use is estimated to be $0.05 per loaf. The supplier, Easton Bakeries, in an effort to induce high consumption offers a discount structure as follows: Cost per loaf for first 50 loaves = $0.30 Cost per any loaf over 50 loaves = $0.20 The fixed cost of a procurement from the bakery = $5.00 a. Show the expected daily profit as a function of the number of loaves of bread ordered per day. b. What quantity of bread should be purchased per day? c. Outline how you would determine the daily loss in profit (compared with the optimal strategy) that would result if the university simply ordered the expected demand? d. What are some complexities that would have to be included to make the problem formulation more realistic?

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