Shirts Unlimited is currently planning for the first quarter of the year sales. Table 1 shows the forecast for the next 12 weeks for their three top products: plain, funny, and sport shirts. Table 1: Demand Forecast for Shirts Unlimited Week Plain Funny Sports 1 450 250 550 2 390 260 580 3 405 220 480 4 350 340 520 5 390 300 550 6789 380 280 490 415 250 500 375 315 530 350 320 480 10 380 350 500 11 320 250 525 12 350 275 530 The production process takes place in three sequential stages: cutting, sewing, and labeling. In addition, the funny and sports feature goes through an additional stage, in total four sequential stages: cutting, sewing, printing, and labeling. Figure 1 illustrates the four main stages of the production process: Cutting Sewing Printing Labeling *Only applicable for funny and sports Figure 1: Production Process Stages in Shirts Unlimited Each process stage has a capacity due to the machine availability and labor at each of these stages. Table 2 shows the capacities, production requirements, and costs incurred per hour at each stage. Table 2: Capacities and Requirements Cutting Sewing Printing Labeling Plain 0.2 0.5 0 0.05 Funny 0.15 0.4 0.3 0.1 Sports 0.2 0.5 0.5 0.1 Capacities (in hours/week) 250 650 400 125 $/hour 7.5 13.5 15 4.5 The factory also has some inventory costs incurred at the end of the week when shirts are left to the next week's sales. The inventory costs for all types of shirts are $2 per unit. Also, there is a monetary penalty for not meeting the demand sales. The costs of unmet demand is $18 per unit, which involves the loss of reputation, and opportunity cost. Based on the information above, Shirts Unlimited needs to develop an aggregate plan that minimizes the manufacturing costs of its three types of shirts. As part of this exercise answer the following: a) Formulate the mathematical model of this aggregate problem (10 points). Note: For full credit, define the sets, parameters, variables, etc. b) Solve the above model based on the data above. What is the optimal production per week of shirts for each type of shirt? Note: You may use Excel's Solver or GAMS. (10 points) c) What will happen if additional labor is acquired to do the sewing? The additional capacity of this process would increase to 800 hours per week. Would that change the optimal solution? (5 points) d) What will happen if one of the printing machines failed and now the total capacity is 200 hours per week. Would that change the optimal solution? (5 points) e) Where do you see that variability may impact the aggregate problem for Shirts Unlimited. Please discuss in a few sentences. (5 points)