ABC Corporation produces two electronics products, A and B, which undergo three processes - Proc1, Proc2 and Proc3 - at its production facility. Details of unit processing times, profit, weight and hours available on each process are provided in the table below: Processing Times/unit (in hours) Product Proc1 Proc2 Proc3 Profit/unit ($) Weight/unit (kgs) A 3.0 3.5 3.2 7.8 6.2 B 4.0 2.8 3.5 6.6 5.8 Capacity Available (hours/day) 8000 6000 7500 Table: Process Details The capacity available for each process can be switched from one process to another at a cost of $10/hour e.g., each hour of capacity switched from Proc1 to Proc2 costs $10/hour, from Proc2 to Proc3 costs $10/hour and so on. The maximum number of hours that can be switched between various processes daily is shown in the table below. From Proc1 Proc1 Proc2 Proc3 400 200 To Proc2 Proc3 500 200 400 400 Table: Process Capacity Switching Limits Once the products (A and B) have been processed at the production facility, these are shipped immediately in trucks to the distribution center (DC). No products can be kept at the production facility due to lack of storage space. For shipping, ABC utilizes its own fleet of trucks which are of two types: (1) Volvo and (2) Tata. Each type of truck comes in two sizes - large (L) and small (S). ABC has 2 large and 7 small Volvo trucks and 3 large and 4 small Tata trucks. The weight capacities of different types and sizes of trucks (in kgs) are shown in the table below. Truck Size (in Kgs) Truck Type Volvo L 5000 Tata 4800 S 1500 1500 Table: Weight Capacities of Different Truck Type-Size To meet safety requirements, ABC must follow the following weight related guidelines for loading products into different trucks: (1) the aggregate weight capacity utilization of all large trucks taken together must be equal to the aggregate weight capacity utilization of all small trucks taken together (2) the weight capacity utilization of all Volvo trucks must be equal to the weight capacity utilization of all Tata trucks. Weight capacity utilization is defined as the actual weight carried in a given truck type-size as a proportion of its maximum weight capacity. Formulate an LP model to ensure that ABC maximizes its daily profit. Clearly identify and define all decision variables