2. Suppose you are the production manager for a company that produces three types of spare parts for automobiles. The manufacture of each part requires processing on each of two available machines, Machine-1 and Machine-2. Processing times on each machine for each product as well as the profit values per unit product are given in the following table. PARTS Machine-1 Processing Time (in minutes) Machine-2 Processing Time (in minutes) Profit (in dollars) TYPE-1 7 5 50 TYPE-2 6 4 40 TYPE-3 1 3 80 Machine-1 is available for 4000 minutes, Machine-2 is available for 5000 minutes per month. The quantity of Type-1 parts should be at least twice that of Type-2. The quantity of Type-3 parts can be at most the total quantity of Type-1 and Type-2 parts. Define your decision variables and formulate a linear programming model for the problem so that you can maximize your company's monthly profit with an optimal monthly production plan. (12P)

2. Suppose you are the production manager for a company that produces three types of spare parts for automobiles. The manufacture of each part requires processing on each of two available machines, Machine-1 and Machine-2. Processing times on each machine for each product as well as the profit values per unit product are given in the following table. Machine-1 is available for 4000 minutes, Machine-2 is available for 5000 minutes per month. The quantity of Type-1 parts should be at least twice that of Type-2. The quantity of Type-3 parts can be at most the total quantity of Type- 1 and Type-2 parts. Define your decision variables and formulate a linear programming model for the problem so that you can maximize your company's monthly profit with an optimal monthly production plan. (12P)