IELM4410 Homework 2
Due: 6 Oct. 2015 (Tuesday) in class
Problem 1
Company A is planning to design a key component for their product with company B. Company A will integrate the component with some software and then sell it to customers. Given the short life cycles of such products and long lead times quoted by Company B, Company A only has one opportunity to place an order with Company B prior to the beginning of its selling season. Company A’s demand during the season is normally distributed with a mean of 1,000 and a standard deviation of 600.
Company B’s production cost for the component is $52 per unit and it plans to sell the component for $72 per unit to Company A. Company A incurs essentially no costs associated with the software integration and handling of each unit. Company A sells these units to consumers for $121 each. It can sell unsold inventory at the end of the season in a secondary market for $50 each. The existing contract specifies that once Company A places the order, no changes are allowed to it. Also, Company B does not accept any returns of unsold inventory, so Company A must dispose excess inventory in the secondary market.
1) What is the probability that Company A’s demand will be more than 40% greater than its forecast?
2) Under this contract, how many units should Company A order to maximize its expected profit?
For Questions 3) to 5), assume Company A orders 1,200 units.
3) What are Company A’s expected sales?
4) How many units of inventory can Company A expect to sell in the secondary market?
5) What is Company A’s expected profit?

Problem 2
You are the manager at a furniture store. One of your products is a chair. Weekly demand for the chair is normally distributed with mean 40 and standard deviation 20. The lead time from the assembly plant to your store is two weeks and you order inventory replenishments weekly.