3. (30 pts.) At the beginning of year 1, a new machine must be purchased. The cost of maintaining a machine i years old is given in the Table 1, below. The cost of purchasing a machine at the beginning of each year is given in Table 2 below (each year you have the option of purchasing a new machine or continuing with the same one). There is no trade-in value when a machine is replaced. Your goal is to minimize total cost of having a machine for four years. Model this problem as a shortest path problem by drawing the nodes and the arcs, and showing the appropriate costs on the arcs. (DO NOT solve the problem) Table 1 Age of machine (Year) 1 4 Maintenance Cost (S) 3,000 5,000 9,000 10,000 Year 1 2 4 Table 2 Purchase Cost (S) 17,000 19,000 21,000 25,000

3. ( 30 pts.) At the beginning of year 1 , a new machine must be purchased, The cost of maintaining a machine i years old is given in the Table 1 , below. The cost of purchasing a machine at the beginning of each year is given in Table 2 below (each year you have the option of purchasing a new machine or continuing with the same one). There is no trade-in value when a machine is replaced. Your goal is to minimize total cost of having a machine for four years. Model this problem as a shortest path problem by drawing the nodes and the ares, and showing the appropriate costs on the arcs. (DO NOT solve the problem)