A retailer selling t-shirts has an initial stock of 2000 units and an initial price of $50 to sell them throughout a 15-week summer season. Because of a company policy, the manager can only mark-down the price once by taking 20% off at some point throughout the season. The remaining inventory is sold back to the manufacturer at x dollars. From historical data, the manager knows that the average weekly demand is 100 when price is set at $50 and increases to 140 with 20% mark-down. a) What is the maximum value of x that would make this mark-down profitable? (7 points) b) Should they go ahead and implement the mark-down in the very first week? (Hint: Use the heuristic discussed in class) (3 points) Li (Ctrl)