QUESTION 1 1. At the beginning of year 1, a manufacturing company must purchase a new machine. The cost of purchasing this machine at the beginning of year 1 (and at the start of each subsequent year) is given in the Table. The cost of maintaining this type of machine, depending on its age, is also provided in the Table. Assume that there is trade-in value when a machine is replaced. If the purchased machine is used for 1 year, the trade-in value is 50% of the original purchase price, 30% if used for 2 years, 20% if used for 3 years, 10% trade-in value if used for 4 years. You can get a price discount when you buy a new machine. The goal of this company is to minimize the total cost (which includes the purchase and maintenance costs) of owning and using this type of machine for the next four years. In particular, the company wants to determine the years in which a new machine should be purchased. Formulate and solve a linear network model. Table: Year 3 4 2 380,000 420,000 500,000 Purchase Price 340,000 Maintenance Cost 76,000 100,000 194,000 364,000 . Define the decision variables a. Define the objective function b. Define the constraints c. Determine an optimal solution