TipTop Snowboards in Beech Mountain, NC sell a popular snowboard during the winter ski season. The anticipated demand is normally distributed with a mean of 651 units ano standard deviation of 112 units. Tiptop purchases the snowboard from the manufacturer for $162 and sells the snowboard for $302. Any unsold snowboards at the end of ski season will be sold on clearance for $124. It costs $9 to hold a unit in inventory for the entire ski season. Round all entries to one decimal place (nearest tenth). Enter probabilities and percent changes as percentages rounded to nearest tenth of a percent (e.g. 0.7146 should be entered as 71.6%) a) Compute the optimal number of units that TipTop should order: units. b) Compute the probability of a stockout given the optimal order quantity, i.e. that demand exceeds the order quantity. %. c) Compute the optimal expected profit associated with the order quantity from part (a): d) Given the optimal order quantity, how many units does TipTop expect to sell on clearance (on average)? units. Suppose that Tip Top's supplier is willing to offer a rush production and shipping option which will allow TipTop a second order opportunity. This will allow Tip Top to assess the winter ski season and order more snowboards if necessary once they observe the demand. However, to offset the cost of the flexible capacity investment, the supplier will charge $176 for units ordered in the second order. e) Compute the optimal order quantity for the initial order: units. f) Compute the new optimal expected profit: $ g) Compute the percent increase in optimal expected profits for Tiptop if using the quick response option compared to your answer in Part c): %