The Silky Shirts Company based in Thailand makes silk women's shirts for a retailer in the U.S. It costs Silky $30 to make each shirt. Silky sells them to the retailer for $50 and the shirts retail for $100. The retailer estimates that it can sell an average of 800 shirts with a standard deviation of 400 at this price per season (normally distributed). The retailer sells all remaining shirts for $20 at the end of the season.

a)If Silky had its own stores, and could make and sell (at the same retail price as above) its own shirts in its own stores instead of needing the retailer as a middleman, how many shirts would it order assuming demand remained the same as above?

b)Silky wants to induce the retailer to order as many shirts as the integrated company would order in Part a). One strategy that Silky is considering is to offer a "buy-back" contract to the retailer, in which case Silky will purchase back any unsold shirts by the end of the season (the retailer no longer sells the remaining shirts by itself). At what price would Silky have to buy back the unsold shirts to induce the retailer to order as many shirts as the integrated company would order in Part a)?