EAGLES is a large company that produces lenses for cameras in military applications. Four types of lenses are made in the three plants in the system. Each plant can produce any of the four lens types, although each plant has its own individual constraints and unit costs. These constraints cover labor and machining restrictions, and the specific values are given in Tables 1-3. Note that even though the products are identical in the three plants, different production processes are used and thus the products use different amounts of resources in different plants EAGLES has 3 major customers (CANCO, SONco, and XERco) for its products. The maximum sales for each customer-product pair are given below. Maximum product sales (number of units) Customers Products CANco SONco XERco small 200 medium 300 500 200 400 300 400 large precision 200 200 300 300 400 Product sales prices are given in Table 4, and the shipping costs from each plant to each customer are detailed in Table 5. Table 6 contains the production costs for each product-plant pair. The last row of Tables 1-3 specifies the availability of labor and hours All shipping from plants 1 and 2 that goes to CANco or SONco must go through a special inspection. These units are sent to a central site, inspected, and then sent to their destination. This special inspection site may inspect at most 1,500 pieces. The corporation controls the material that goes in the lenses; the material requirements for each product are given in the last column of Tables 1-3. A total of 3,500 pounds of material is available for the entire system (that is, all three plants) Table 1. Product-resource constraints Plant Resources Labor Products Machine Material Hours/unit hours/unit Ib/unit small 3 1 medium large precision TOTAL AVAIABLE 6000 3 8.5 1.1 4 1.2 4 1.3 10000 Table 2. Product-resource constraints Plant 2 Resources Labor Hours/unit hours/unit lb/unit 3.5 3.5 Machine Material Products small 7 1.1 medium large precision TOTAL AVAILABLE 5000 7 1 4.5 8 1.1 4.5 9 14 12500 Table 3. Product-resource constraints Plant 3 Resources Labor Hours/unit hours/unit Ib/unit 3 Machine Material Products small 7.5 1.1 medium large precision TOTAL AVAILABLE 3000 3.5 7.5 1.1 4 8.5 1.3 4.5 8.5 1.3 6000 Table 4. Product sales price ($) per unit Customers Products CANCO SONCO XERco small medium 18 large precision 29 17 16 16 18 17 22 22 23 26 27 Table 5. Shipping costs (S) per unit Customers Plants CANco SONCO XERco Plant 11 1.6 1.1 Plant 21.2 1.5 1 Plant 31.4 1.5 1.3 Table 6. Production costs (S) per unit Plants Products Plant small Plant 2 Plant 3 14 medium 16 18 13 14 17 15 large precision 26 20 19 24 23 Your job is to determine a recommendation for the company. A recommendation must include a plan for production and shipping as well as the cost and revenue generated from each plant. In addition, you should also address the following sensitivity analysis issues in your recommendation. Note that you should address the following issues by using sensitivity analysis results as much as possible. QUESTIONS a) If you could get more material, how much would you like without changing the optimal basis and what would you be willing to pay in total? EAGLES is a large company that produces lenses for cameras in military applications. Four types of lenses are made in the three plants in the system. Each plant can produce any of the four lens types, although each plant has its own individual constraints and unit costs. These constraints cover labor and machining restrictions, and the specific values are given in Tables 1-3. Note that even though the products are identical in the three plants, different production processes are used and thus the products use different amounts of resources in different plants EAGLES has 3 major customers (CANCO, SONco, and XERco) for its products. The maximum sales for each customer-product pair are given below. Maximum product sales (number of units) Customers Products CANco SONco XERco small 200 medium 300 500 200 400 300 400 large precision 200 200 300 300 400 Product sales prices are given in Table 4, and the shipping costs from each plant to each customer are detailed in Table 5. Table 6 contains the production costs for each product-plant pair. The last row of Tables 1-3 specifies the availability of labor and hours All shipping from plants 1 and 2 that goes to CANco or SONco must go through a special inspection. These units are sent to a central site, inspected, and then sent to their destination. This special inspection site may inspect at most 1,500 pieces. The corporation controls the material that goes in the lenses; the material requirements for each product are given in the last column of Tables 1-3. A total of 3,500 pounds of material is available for the entire system (that is, all three plants) Table 1. Product-resource constraints Plant Resources Labor Products Machine Material Hours/unit hours/unit Ib/unit small 3 1 medium large precision TOTAL AVAIABLE 6000 3 8.5 1.1 4 1.2 4 1.3 10000 Table 2. Product-resource constraints Plant 2 Resources Labor Hours/unit hours/unit lb/unit 3.5 3.5 Machine Material Products small 7 1.1 medium large precision TOTAL AVAILABLE 5000 7 1 4.5 8 1.1 4.5 9 14 12500 Table 3. Product-resource constraints Plant 3 Resources Labor Hours/unit hours/unit Ib/unit 3 Machine Material Products small 7.5 1.1 medium large precision TOTAL AVAILABLE 3000 3.5 7.5 1.1 4 8.5 1.3 4.5 8.5 1.3 6000 Table 4. Product sales price ($) per unit Customers Products CANCO SONCO XERco small medium 18 large precision 29 17 16 16 18 17 22 22 23 26 27 Table 5. Shipping costs (S) per unit Customers Plants CANco SONCO XERco Plant 11 1.6 1.1 Plant 21.2 1.5 1 Plant 31.4 1.5 1.3 Table 6. Production costs (S) per unit Plants Products Plant small Plant 2 Plant 3 14 medium 16 18 13 14 17 15 large precision 26 20 19 24 23 Your job is to determine a recommendation for the company. A recommendation must include a plan for production and shipping as well as the cost and revenue generated from each plant. In addition, you should also address the following sensitivity analysis issues in your recommendation. Note that you should address the following issues by using sensitivity analysis results as much as possible. QUESTIONS a) If you could get more material, how much would you like without changing the optimal basis and what would you be willing to pay in total