Good Shoes Company manufactures ski boots for children each pair of which costs $40 to manufacture. Good Shoes sells the boots to a well-known sports goods retailer and the retailer sells each pair for $100. Any boots not sold (by the retailer) during the season are sold to a discount retailer for $20 a pair. Demand during the season is assumed to have a Normal distribution with a mean of 850 and a standard deviation of 350.

1. What should the manufacturer charge the retailer per pair to maximize its expected profits? Assume that Good Shoes will consider a price from the following set: (60,65,70,75,80,85 90,95), i.e., The manufacturer's price will be either $60, or $65 or $70, or ......,,$95).