5. (30 points) Consider a new apparel item which retails for $45, costs $25 to procure, and can be sold at a clearance price of $20 after it is no longer (a) Find the optimal stocking quantity and the resulting expected profits (b) Find the optimal stocking quantity and the resulting expected profits fashionable. if demand D N (1000, 2502) if demand D~Uniform(500, 1500) Hint: it may be helpful to make use of LU(a,b) (x) from Problem 2. (c) Now instead consider 100 retail locations owned by the same com- pany, each with its own (independent) demand DiUniform(5,15); easy to see that the optimal stocking quantity at each location is 1% of that found in part (b) and the total expected profits across all locations is the same as that found in part (b). Briefly justify why this is the demands across locations are independent. It should be case. 5. (30 points) Consider a new apparel item which retails for $45, costs $25 to procure, and can be sold at a clearance price of $20 after it is no longer (a) Find the optimal stocking quantity and the resulting expected profits (b) Find the optimal stocking quantity and the resulting expected profits fashionable. if demand D N (1000, 2502) if demand D~Uniform(500, 1500) Hint: it may be helpful to make use of LU(a,b) (x) from Problem 2. (c) Now instead consider 100 retail locations owned by the same com- pany, each with its own (independent) demand DiUniform(5,15); easy to see that the optimal stocking quantity at each location is 1% of that found in part (b) and the total expected profits across all locations is the same as that found in part (b). Briefly justify why this is the demands across locations are independent. It should be case