(Monte Carlo analysis) You have been asked to advise Milano Market on their Easter cake inventory order and pricing policy. The store currently orders 500 boxes of colomba Easter dove cake (handmade by a master pastry chef) from Italy for delivery 3 weeks before Easter. Each box costs the store $9 and is initially priced for sale at $39. On Good Friday, all unsold boxes are offered for sale at $21 or less. Any unsold cakes on Easter Sunday are thrown out with no benefit to to the company. Assume that demand in the three weeks before Good Friday is randomly uniformly distributed between 300 to 450 boxes. Demand from Good Friday to Easter Sunday is forecasted to be randomly uniformly distributed in the following manner: the lower bound is given by 0.1x (1200-3p) and the upper bound is given by 0.2x(1200-3p) where p is the sale price offered on boxes on Easter weekend ($21 or less). (a) What is the number of boxes that the store should expect to sell, assuming that the Easter weekend price is $21? (b) Assume that you change the order from 500 boxes to the number of boxes you computed in (a). Construct a simulation of 10,000 trials to evaluate the distribution of profit, assuming the Easter weekend price is set at $21. What is average profit over your trials? What is the confidence interval within which profit is likely to fall 95% of the time? (c) Graph the distribution of profit in your simulation. How does it differ from the uniform distribution? (d) How many boxes would you recommend that the store orders to maximize expected profit? (Assume for now that the Easter weekend price is set at $21). Is this quantity equal to the number computed in (a)? If equal, why is it equal? If not, why not? (e) Now assume that the order is equal to the number of boxes you computed in (a)? What sale price below $21 would you set for the unsold boxes during Easter weekend to maximize expected pro t? Should this sale price depend on the number of unsold boxes at the beginning of Good Friday? If yes, why? If not, why not? (f) Now assume that the company's food waste collection contractor charges the store $1 for every unsold box that gets thrown out at the end of the day. How would you modify your response to part (e) to account for the food waste charge?