Topic (Product pooling) Question: Stationery Central's product collection include two types of binder: two-ring and four-ring. The two-ring binder is useful for managing notes as they are easy to add or remove materials quickly; four rings, on the other hand, are preferred for visual portfolio as they keep all the pages in line and are durable under heavy use as the pages are far less likely to rip out. The binders are identical in design and material as well as the holding capacity; the only difference is in the rings in place. The manager of Stationery Central is now considering detachable rings so that a single type of binder can satisfy both needs. She is very interested in quantifying the benefits of having a single product instead of two, while continuing to satisfy existing demand. Therefore she wants to calculate the expected profit under the two scenarios: i) selling two-ring and four-ring binders separately, and ii) selling a single type of binder with detachable rings. Demand for the two-ring binder is normally distributed with mean 3580 and standard deviation 1210. Demand for the four-ring binder is normally distributed with mean 2370 and standard deviation 890, and the two demands are independent. Each binder has a price of 2.00 and a salvage value of 0.20. Assume that the cost of the rings itself is negligible, so that the cost of producing two-ring / four-ring binders are both 0.80, but the new binder with detachable rings would increase the cost to 0.85. Help the manager of Stationery Central in her calculations by answering the following questions. Please explain how you came to your answers. 1) Calculate the underage cost, overage cost and the critical ratio for the three different types of binders. 2) What is the optimal order quantity for each type of binders? 3) What are the expected sales in the case of scenario i)? And in scenario ii)? 4) What is the expected leftover inventory in both scenarios? 5) Calculate the expected profit in both scenarios and comment on how they compare. Provide a qualitative explanation of this difference in profit