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 aNormal distribution with a mean of 850 and a standard deviation of 350. The problem in the class is uniform

1. What should the manufacturer charge the retailer per pair to maximize its expected profits? Assume that the 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).

b. At the price charged given in (a) above by the manufacturer, what will be:

i.) the manufacturer's profit

ii) the retailer's order size?

iii) the retailer's expected profit?

iv) the expected number of units sold by the retailer? Mean of the distribution

v) the expected number of units salvaged?

1. Now assume that the manufacturer and the retailer is an integrated single company. Please answer the following for the integrated company. What is

i)the optimal production quantity?

ii)the expected number of unit sold?

iii) the expected number of units salvaged?

iv) the expected profit of the integrated company?

1. What conclusion do you reach when you compare the total expected profit under the scenario given in (b) above (that is, the manufacturer's profit + the retailer's profit) to that of the scenario given in (c) above?