Question

One of the specialties at Dixie’s Cafe is vegetable stew, which simmers over a low flame all day. Since the cooking time is so long, Dixie must decide in the morning how many servings of the stew to cook for that night’s dinner service. Moreover, the stew cooked on a given day cannot be served the next day; it must be thrown away. Vegetable stew is the highest-profit item on the menu at Dixie's Cafe. It earns Dixie a profit of $8. Demand for in-flight meals Cumulative d Probability f(d) Probability F(d) 40 0.01 0.01 41 0.03 0.04 42 0.04 0.0843 0.05 0.1344 0.08 0.2145 0.09 0.346 0.12 0.42 47 0.13 0.55 48 0.17 0.7249 0.12 0.8450 0.08 0.9251 0.03 0.95 52 0.02 0.9753 0.02 0.01 54 0.99 1 serving, whereas all the other items earn a profit of $4. Customers who want stew but find it out of stock will order one of these other items. The ingredients for one serving of stew cost the Cafe $2.50. A) First suppose that the demand for stew on a given evening is normally distributed with a mean of 18 and a variance of 16. How many servings of stew should Dixie prepare in the morning? (Fractional servings are OK). What is the expected cost (ingredients and lost profit) of the optimal solution? B) Now suppose that the demand is distributed as an exponential random variable with mean 18. How many servings should Dixie prepare?

Answer 1

Answer:

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