Jill estimates that the annual demand of a part can be approximated as a Poisson distribution with parameter value of 15. It takes 50 days to receive a replenishment order. The firm uses an annual interest rate of 10% and each unit of this part costs $100. The ordering cost is $20 per order. A shortage causes the customer to buy from competition, the cost of which is estimated to be S50. Suggest an appropriate inventory model that Jill should use, indicate the reasons for your choice, and solve for the corresponding how much' and 'when' questions?