A fundamental decision for a manufacturing company is the product mix decision, which consists of the quantity of each product to make in order to maximize profitability (or minimize losses) for the organization. XYZ Corp. manufactures five different products: A, B, C, D and E. Table 1 presents the product prices, material costs and the weekly demand. Table 2 presents the labor requirements and labor availability for each of the four work centers in the XYZ manufacturing plant. The labor requirements indicate how much labor time is required to manufacture one of each product. The available labor indicates that two full-time employees each are assigned to work centers 1 and 4. Work center 2 has one full-time employee, while work center 3 has three full- time employees. In order to simplify the problem, assume that setup times in the work centers and efficiencies are not relevant. Total operating expenses per week are $14,000 (not including cost of materials). 30 TABLE 1: Price, Material Cost, and Demand Product Price Material Cost M 90 9128 101 3 5 224 | 84 146 80 Weekly Demand 120 100 100 D TABLE 2: Labor requirements and Labor Availability Product Work Center 1 Work Center 2 Work Center 3 15 mins. 0 mins 20 mins. B 10 mins. 7 mins. 10 mins. 15 mins. 7 mins. 13 mins. D O mins. 60 mins. 3 mins. 0 mins. 23 mins 15 mins Time available 80 hours 40 hours 120 hours Work Center 4 6 mins. 15 mins. 10 mins. 4 mins. 6 mins. 80 hours How much of each product should we manufacture to maximize profitability? What will our weekly profit be for this product mix