A confectioner sells novelty birthday cakes in Marks & Spencer (M&S) at €15 each. The marginal production cost for the confectioner is €2.50 per cake. At M&S, the cakes are priced at €29 and the expected demand over the next two months to be normally distributed, with a mean of 8,000 and a standard deviation of 2,000. M&S places a single order with the confectioner for delivery at the beginning of the two-month period. Currently, M&S discounts any unsold cakes at the end of two months down to €5, and any cakes that did not sell at full price sell at this price.
a. How many cakes should M&S order? What is its expected profit? How many cakes does it expect to sell at a discount?
b. What is the profit that the confectioner makes, given M&S’s actions?
c. A plan under discussion is for the confectioner to refund M&S €7 per cake that does not sell during the two-month period. As before, M&S will discount them to €5 and sell any that remain. Under this plan, how many cakes will M&S order? What is the expected profit for M&S? How many cakes are expected to be unsold? What is the expected profit for the confectioner? What should the confectioner do?