Big$10$Sweaters com is a new company started last year by two recent college graduates. The idea behind the company was simple. They will sell premlum logo sweaters for Big Ten colleges with one major, unlque feature. This unique feature is a special large monogram that has the customer's name, major, and year of graduation. The sweater is the perfect glft for graduating students and alumni, particularly avid football fans who want to show support during the football season. The company is off to a great start and had a successful first year while selling to only a few schools. This year they plan to expand to a few more schools and target the entire Big Ten Conference withln three years.

You have been hired by Big$10$Sweaters.com and need to make a good Impression by making good supply chain decisions. This is your big opportunity with a startup. There are only two people in the firm and you were hired with the prospect of possibly becoming a principal in the future. You majored in supply chaln $($operations$)$ management in school and had a great internship at a big retaller that was getting into Internet sales. The experlence was great, but now you are on your own and have none of the great support that the blg company had. You need to find and analyze your own data and make some blg decislons. Of course, Rhonda and Steve, the partners who started the company, are knowledgeable about this venture and they are going to help along the way.

Rhonda had the idea to start the company two years ago and talked her friend from business school, Steve, Into joining her. Rhonda is into web marketing, has a degree in computer sclence, and has been working on completing an online MBA. She is as much an artist as a techle. She can really make the website sing.

Steve majored in accounting and likes to pump the numbers. He has done a great job of keeping the books and selling the company to some small venture capital people in the area. Last year, he was successful in getting them to invest $\backslash$$$2,000,000$ in the company $($a onetime investment$).$ There were some significant strings attached to this investment in that it stipulated that only $\backslash (\backslash$$ $100,000\backslash )$ per year could go toward paying the salary of the two princlpals. The rest had to be spent on the website, advertising, and inventory. In addition, the venture capital company gets $28$ percent of the company profits, before taxes, during the first four years of operation, assuming the company makes a profit.

Your first job is to focus on the firm's inventory. The company is centered on selling the premlum sweaters to college football fans through a website. Your analysis is important since a significant portion of the company's assets is the inventory that it carries.

The business is cyclic, and sales are concentrated during the period leading up to the college football season, which runs between late August and the end of each year. For the upcoming season, the firm wants to sell sweaters to only a few of the largest schools in the Midwest region of the United States. In particular, they are targeting The Ohlo State University $($OSU$),$ the University of Michigan $($UM$),$ Michigan State University $($MSU$),$ Purdue University $($PU$),$ and Indiana University $($IU$).$ These five schools have major football programs and a loyal fan base.

The firm has considered the Idea of making the sweaters in thelr own factory, but for now they purchase them from a supplier in China. The prices are great, but service is a problem since the supplier has a $20-$week lead time for each order and the minimum order size is $5,000$ sweaters. The order can consist of a mIx of the different logos$,$ such as $2,000$ for OSU, $1,500$ for UM$,750$ for MSU, $500$ for PU$,$ and $250$ for IU$.$ Within each logo sub lot, sizes are allocated based on percentages and the supplier suggests $20$ percent $\backslash ($ X $\backslash )-$large, $50$ percent large, $20$ percent medium, and $10$ percent small based on their historical data.

Once an order is recelved, a local subcontractor applies the monograms and ships the sweaters to the customer. They store the Inventory of sweaters for the company in a small warehouse area located at the subcontractor.

This is the company's second year of operation. Last year they only sold sweaters for three of the schools, OSU, UM$,$ and PU$.$ They ordered the minimum $5,000$ sweaters and sold all of them, but the experlence was palnful since they had too many UM sweaters and not enough for OSU fans. Last year they ordered $2,440$ OSU, $1,790$ UM$,$ and $770$ PU sweaters. Of the $5,000$ sweaters, $439$ had to be sold at a steep discount on eBay after the season. They were hoping not to do this again. In addition to the cost data, you also have some demand information, as shown In Exhibit $20\mathrm{.}13.$ The exact sales numbers for last year are given. The exhibit indicates the retall or "full price" sales for the sweaters that were sold for $\backslash (\backslash$$ $131\backslash )$ each. Sweaters that we had at the end of the season were sold through eBay for $\backslash (\backslash$$ $45\backslash )$ each and were not monogr