You are in the business of selling winter ski equipment. One of the manufacturers you work with has just come out with a new style of ski, the Mogul Monster. You can sell a pair of Mogul Monster skis for $700 and a pair costs you $250 when you buy a pair from the manufacturer. The manufacturer is willing to buy any unsold pairs of skis from you for $75 at the end of the season. The bad news is that the demand is uncertain, though you estimate that the demand will have a mean of 9 pairs of skis and that the demand will follow a Poisson distribution. HINT: Use POISSON.DIST to generate p.m.f. and c.d.f.. a) How many pairs of skis should you buy if you want to maximize your expected profit? b) If you buy that many pairs of skis, what is the expected profit? c) If you buy that many pairs of skis, how many pairs of skis do you expect to sell? d) If you buy that many pairs of skis, how many pairs of skis do you expect to return to the manufacturer at the end of the season? e) Plot the expected profit (on the Y axis) versus the number of pairs of skis you buy from the manufacturer (on the X axis), letting the number you buy go from 0 to 30 (in an increment of 1). f) Find all values of the number of pairs of skis you buy from the manufacturer such that your expected profit is within 10% of the value you found in part (b). g) To the nearest $1.00, what is the smallest refund on unsold skis that the manufacturer must offer for you to be induced to buy one more pair of skis from the manufacturer