PS Handout #1 - IND315 Operations Research, Fall 2022 6 6. Resource Allocation Problem Consider a manufacturing facility that produces five different products using four machines. The scarce resources are the times available on the machines, and the alternative activities are the individual production volumes. The machine requirements in hours per unit are shown for each product in Table 1. With the exception of product 4, which does not require machine 1, each product must pass through all four machines. The unit profits are also shown in the table. Table 1: Machine Data and Processing Requirements (Hours per unit) Quantity Product 1 Product 2 Product 3 Product 4 Machine Product 5 M1 4 1.2 1.3 0.7 0 0.5 M2 5 0.7 2.2 1.6 0.5 1.0 M3 3 0.9 0.7 1.3 1.0 0.8 M4 7 1.4 2.8 0.5 1.2 0.6 Unit profit ($) 18 25 10 12 15 The facility has four machines of type 1, five of type 2, three of type three and seven of type 4. Each machines operates 40 hours per week. Construct a mathematical model that determines the optimum weekly production quantities for the products that will maximize the total profit.

6. Resource Allocation Problem Consider a manufacturing facility that produces five different products using four machines. The scarce resources are the times available on the machines, and the alternative activities are the individual production volumes. The machine requirements in hours per unit are shown for each product in Table 1. With the exception of product 4, which does not require machine 1, each product must pass through all four machines. The unit profits are also shown in the table. Tahle 1. Marhine Nata and Proreceine Ranniramante (Houre nar unit) The facility has four machines of type 1, five of type 2, three of type three and seven of type 4. Each machines operates 40 hours per week. Construct a mathematical model that determines the optimum weekly production quantities for the products that will maximize the total profit