The sports merchandise company, Fanatics is a maker of sports apparel. It is similar to fast- fashion retailers like Zara, integrating design and manufacturing with distribution to fulfill orders within hours. To produce a typical jersey, a sequence of three activities must be undertaken in Fanatics. The first step involves cutting fabric which takes 5 minutes per jersey. The second step involves embroidering eight different pieces (lettering, numbering, logo, etc.) onto the jersey. Each of these pieces takes 45 seconds to embroider. Once all eight pieces have been embroidered, the jersey moves to the final step, where it is sewn together. This activity takes about 2 minutes per jersey. For simplicity, assume each order is for one jersey. During the first week, the manufacturer employed one worker at each activity and ran the production process 8 hours per day, five days per week. The total number of jerseys ordered during the first week was 3200 jerseys, and Michael Rubin, the manager, noticed there was a fairly large backlog. He needs your help to figure out a cost-effective plan for the upcoming weeks (weeks 2 through 4). His order projections are as follows: Orders (jerseys) 3200 Week 2 3 3600 4 4000 a) During the first week, what was the process capacity (jerseys/week)? b) Starting in week 2, Mr. Rubin wants to increase the number of workers performing each activity to make sure he can produce jerseys fast enough to satisfy orders. Assuming that each worker is dedicated to a particular activity (no cross training), what is the minimum number of workers at each step in order to achieve no remaining backlog (including the backlogs from the first week) by the end of week 4? Note: Mr. Rubin can only change the number of workers once at the beginning of week 2, and he must choose a whole number of workers - no fractional workers. For the remaining parts, assume you have the number of resources at each step that you computed in part (c) for the final three weeks. c) Draw an inventory build-up diagram of the jersey orders over all four weeks. Assume orders flow into the process continuously. At what point in time will the backlog final be cleared?