Problem 2: (15 points) Suppose that you serve two types of demands. Both follow Normal distributions with (mean, standard deviation) being (100, 30) and (200, 40) respectively. You can build unique products to serve each demand separately, in which case the cost of building either one is $15 per unit. You may also build a common product to serve both demands, and the cost will be $20 per unit. There is no backlog cost. Your goal is to keep the stock out probability at 1% for both demands regardless your product choice (you can use 2a = 20.99 = 2.33 for 1 a = 0.01). Question: Determine whether you want to build separate or common product when p = 1, 0, and 1. Determine the amount of the cost saved in comparison with the alternative choice.