The Hamlet of Pella is preparing for its annual Tulip festival. The organizing committee is grappling with the issue of determining the quantity and price of the commemorative T-shirts it plans to sell. The design has already been agreed upon and a manufacturer has agreed to supply the shirts at 4.50 dollars each. The committee has to decide whether to sell these T-shirts at 10 dollars or 15 dollars each. There is, of course, randomness in the demand for these T-Shirts. The committee predicts that at a price of 10 dollars, the demand is normally distributed with a mean of 800 and a standard deviation of 50. However, at a price of 15 dollars, the mean will drop to 650 and the standard deviation will increase to 200. Assume that there is no salvage value or shortage cost.
1) At the price of 10 dollars, determine the optimal number of T-shirts the committee should purchase.
2) What is the resulting expected profit?
3) If the committee implements the strategy with the price of 10 dollars, what percentage of customers will not be able to obtain a T-Shirt?
4) At the price of 15 dollars, determine the optimal number of T-shirts the committee should purchase.