Skimore is a retail chain that specializes in the sales of Alpine skis. Skimore sells its own brand of skis in three styles: S, DX, and LX. Per pair, the three skis cost Skimore $260, $400, and $480, respectively, to purchase from the manufacturer. Throughout the selling season, the chain will sell pairs of skis to consumers for $300, $450, and $550, respectively. At the end of the season, if the skis are not sold, they will be sold (in pairs) to a liquidator for $50, $230, and $290, respectively. Skis are purchased from the manufacturer once, before the selling season. Skimore has identified two distinct segments of customers who purchase from the store: early buyers who prefer top-of-the-line skis (Elite) and bargain-hunters (Hunters). The Elite arrive first in the season, and you may assume that all Hunters arrive at the end of the season, after all the Elite. The two customer segments have different preferences for skis. Elite prefer to buy LX skis. If LX skis are sold out, they will always buy DX skis, and if LX and DX skis are sold out, Elite will always buy S skis. Hunters prefer S, then DX, and will not buy LX skis. Assume each customer buys one pair of skis. Skimore expects to see 5000 buying customers during the season, of which 60% are Elite and 40% are Hunters. Skimore's purchasing manager plans to begin its season with 1300 pairs of LX skis, 2200 pairs of DX skis, and 1900 pairs of S skis, but he is considering alternate order quantities.

a. Construct a well-designed spreadsheet model to calculate the total profit for the base case given.

b. If a total profit of $250,000 is desired, what selling price of DX skis is necessary? Make sure to show screenshots and/or give full explanation of your solution approach.