A confectioner sells novelty birthday cakes in Marks and 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 $down29 and the expected demand over the next two months will 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.

1. How many cakes should M&S order? What is its expected profit? How many cakes does it expect to sell at a discount?