Santa Inc. is currently making its inventory decisions for the upcoming 2024 winter holiday season based on the newsvendor model (no need to hustle too hard to make money during the holiday season). One of the item under consideration is a miniature Christmas house. Each house will be sold at the retail price of $30. The wholesale price of the miniature Christmas house (the price at which Santa Inc. will buy the item from Elf GmbH) is $8 per unit. It costs Elf GmbH $2 per unit to manufacture the miniature Christmas house. Leftover inventory at the end of the selling season will be disposed and Santa Inc. receives no value. Demand for the miniature Christmas house is currently forecasted to be normally distributed with mean of 20,000 units and standard deviation of 5,000 units. (a) Assume that Santa Inc. enters into a buy-back contract with Elf GmbH. Under this contract, Elf GmbH will buy back any leftover inventory at the end of the selling season for $6 per unit. If Santa Inc. wishes to maximize its expected profit from the miniature Christmas house, how many units should it order under the buy-back contract? (b) What is the buy-back price