Urgent : Operation Research - Inventory Model

Step by step answer please

15. Jill, the office manager of a desktop publishing outfit, stocks replacement toner cartridges for laser printers. Demand for cartridges is approximately 30 per year and is quite variable (i... can be represented by the Poisson distribution). Cartridges cost $100 each and require 3 weeks to obtain from the vendor. Jill uses a (0,r) approach to control stock levels. (a) If Jill wants to restrict replenishment orders to twice per year on average, what batch size should she use? Using this batch size, what reorder point r should she use to ensure a service level (i.e., probability of having the cartridge in stock when needed) of at least 98 percent? (b) If Jill is willing to increase the number of replenishment orders per year to six, how do and r change? Explain the difference in r. (c) If the supplier of toner cartridges offers a quantity discount of $10 per cartridge for orders of 50 or more, how does this affect the relative attractiveness of ordering twice per year versus six times per year? Try to frame your answer in definite economic terms