answer letters a-e please in that order.

a. 6. [20 points) A brand of men's wallets are sold for $20 per unit by a retailer. The retailer buys the wallets from a manufacturer for $11 per unit. The manufacturing cost for the manufacturer is $4 per unit. The average monthly demand is 1500 units and the standard deviation is 300. The demand is assumed to be normally distributed. if the retailer and the manufacturer are operating as independent organizations, what is the order size that maximizes the retailer's profit? b. In above scenario, what is the expected profit for retailer? C. If the actual order quantity should be rounded to the closest 100 units, what is the total supply chain expected profit? d. Consider that the retailer acquired the manufacture. What is the order size for the vertically integrated supply chain? What is the expected profit for the vertically integrated supply chain? es