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 premium logo sweaters for Big Ten colleges with one major, unique feature. This unique feature is a special large monogram that has the customer$$s name, major, and year of graduation. The sweater is the perfect gift for graduating students and alumni, particularly avid football fans who want to show support during the football season. The company is off to a great start and had a successful first year while selling to only a few schools. This year they plan to expand to a few more schools and target the entire Big Ten Conference within three years.You have been hired by Big$10$Sweaters.com and need to make a good impression by making good supply chain decisions. This is your big opportunity with a startup. There are only two people in the firm and you were hired with the prospect of possibly becoming a principal in the future. You majored in supply chain $($operations$)$ management in school and had a great internship at a big retailer that was getting into Internet sales. The experience was great, but now you are on your own and have none of the great support that the big company had. You need to find and analyze your own data and make some big decisions. Of course, Rhonda and Steve, the partners who started the company, are knowledgeable about this nture and they are going to help along the way.Rhonda had the idea to start the company two years ago and talked her friend from business school, Steve, into joining her. Rhonda is into web marketing, has a degree in computer science, and has been working on completing an online MBA. She is as much an artist as a techie. She can really make the website sing.Steve majored in accounting and likes to pump the numbers. He has done a great job of keeping the books and selling the company to some small venture capital people in the area. Last year, he was successful in getting them to invest $$2,000,000$ in the company $($a onetime investment$).$ There were some significant strings attached to this investment in that it stipulated that only $$100,000$ per year could go toward paying the salary of the two principals. The rest had to be spent on the website, advertising, and inventory. In addition, the venture capital company gets $26$ percent of the company profits, before taxes, during the first four years of operation, assuming the company makes a profit. Your first job is to focus on the firm$$s inventory. The company is centered on selling the premium 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 Ohio 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 their 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 X$-$large, $50$ percent large, $20$ percent medium, and $10$ percent small based on their historical data.Exhiblt $20\mathrm{.}13$

r$347$ swesters wer

Once an order is received, 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$$s second year of operation. Last year they only sold sweaters for three of the schools, OSU, UM$,$ and PU$.$ They ordered the minimum $5,000$ sweaters and sold all of them, but the experience was painful since they had too many UM sweaters and not enough for OSU fans. Last year they ordered $2,230$ OSU, $1,820$ UM$,$ and $950$ PU sweaters. Of the $5,000$ sweaters, $347$ had to be sold at a steep discount on eBay after the season. They were hoping not to do this again.For the next year, you have collected some data relevant to the decision. Exhibit $20\mathrm{.}12$ shows cost information for the product when purchased from the supplier in China. Here we see that the cost for each sweater, delivered to the warehouse of our monogramming subcontractor, is $$55\mathrm{.}83.$This price is valid for any$*347$ quantity that we order above $5000$ sweaters. This order can be a mix of sweaters for each of the five schools we are targeting. The supplier needs $20$ weeks to process the order, so the order needs to be placed around April $1$ for the upcoming football season. See Exibit $20\mathrm{.}12[$screenshot$]$