Frank Rogers owns a small firm that manufactures "Rogers Sunglasses." Frank has been approached by REI about selling a seasonal sunglass design through their stores. Frank offers REI two purchasing options:

• Option 1: Frank sells the sunglasses to REI for $60 each and agrees to credit REI $35 for each pair REI returns to Frank at the end of the season (because those units did not sell). Since styles change each year, there is essentially no value in the returned merchandise.
• Option 2: Frank offers a price of $50 for each unit, but no longer accepts returns. In this case, REI throws out unsold units at the end of the season.

Assume the annual demand for this design will be normally distributed with mean of 200 and standard deviation of 125. REI will sell those sunglasses for $100 each. Frank's production cost is $25

(a) (10 points) How many pairs of sunglasses should REI buy to maximize their profits under option 1? Option 2?

(b) (10 points) To help REI choose which option to take, you have run a Crystal Ball simulation (see Table 1 on next page). For a given quantity of sunglasses purchased, you simulated demand 1,000 times to estimate how many sunglasses would be sold and how many sunglasses would be left over. Based on this information, and using the calculations you made above for option 1 and option 2, which option will REI choose? (note: You may need to interpolate the values from the table below.For example, if the calculation from part (a) is 177 you would assume 141 would sell (between 140 listed for 175 and 142 listed for 180) and 36 (177-141) would be returned.

(c) (5 points) Suppose REI chooses option 1 and orders 275 units.What is your best estimate of Frank's expected profit?