Let X = damage incurred ($) in a certain type of accident. Possible X values are 0, 2000, 4000, and 9000, with probabilities .7, .15, .1, and .05 respectively. A particular company offers a $500 deductible policy, which means they do not pay the first $500 of any damage incurred. So if you have a $1000 accident, then they will pay for $1000 - $500 of it. If the company wishes its expected profit to be $100, what premium amount should it charge? The premium is what the insurance company charges you for buying insurance.

Haley photocopying purchases a paper from an out-of-state vendor. average weekly demand for paper is 150 cartons per week for which haley pays $15 per carton. in bound shipments from the vendor average 1000 cartoons with an average lead time of 3 weeks. haley operates 52 weeks per year; it carries a 4-week supply of inventory as safety stock and no anticipation inventory. the vendor has recently announced that they will be building a faculty near haley photocopying that will reduce lead time to one week. further, they will be able to reduce shipments to 200 cartons. haley believes that they will be able to reduce safety stock to a 1-week supply. what impact will these changes make to haley’s average inventory level and its average aggregated inventory value?