Inbox (94 messages, 54 unread) - MC Q- Design Layout References Mailings + Share Review >> Insert Home Calibri (Body) 11 A. A A. A Paste B T U .be X, X A. Paragraph Styles Problem 2 (4 points) At the beginning of year one, a manufacturing company purchases a new machine. The cost of buying this machine at the beginning of year 1,2,3, and 4 (at the start of each subsequent year) is given in Table 1. Since the company wants to use up-to-date machines, the company can replace the used machine with a new machine at any time after one year of use. For example, if the company switched to a new machine at the beginning of year two and used it for two years, the total cost would be $ 365 (new machine price + 2 years use - $350 + $ 15). The cost of maintaining this type of machine, depending on its period of use, is also given in Table 2. If the machine used three years, the total of three years of maintenance cost would be $20. Assume that there is no trade-in value when a machine is replaced. 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 (e.g., the end time is the beginning of year 5). In particular, the company wants to determine the years in which a new machine should be purchased. Table 1: New machine price at the beginning of the year. Year 2 3 4 Purchase Price $300 $350 $400 S450 Table 2: Total machine maintenance cost depending on the period of use Year 1 year use 2 years use 3 years use Maintenance Cost S10 $20 $15 4 years use $30 a) Define the decision variables. b) Define the objective function Define the constraints d) Determine an optimal solution Problem 3 (points) The network below shows the flows possible between pairs of six locations, Formulate an LP to find the maximal flow possible from Node 1 to Node 6 Inbox (94 messages, 54 unread) - MC Q- Design Layout References Mailings + Share Review >> Insert Home Calibri (Body) 11 A. A A. A Paste B T U .be X, X A. Paragraph Styles Problem 2 (4 points) At the beginning of year one, a manufacturing company purchases a new machine. The cost of buying this machine at the beginning of year 1,2,3, and 4 (at the start of each subsequent year) is given in Table 1. Since the company wants to use up-to-date machines, the company can replace the used machine with a new machine at any time after one year of use. For example, if the company switched to a new machine at the beginning of year two and used it for two years, the total cost would be $ 365 (new machine price + 2 years use - $350 + $ 15). The cost of maintaining this type of machine, depending on its period of use, is also given in Table 2. If the machine used three years, the total of three years of maintenance cost would be $20. Assume that there is no trade-in value when a machine is replaced. 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 (e.g., the end time is the beginning of year 5). In particular, the company wants to determine the years in which a new machine should be purchased. Table 1: New machine price at the beginning of the year. Year 2 3 4 Purchase Price $300 $350 $400 S450 Table 2: Total machine maintenance cost depending on the period of use Year 1 year use 2 years use 3 years use Maintenance Cost S10 $20 $15 4 years use $30 a) Define the decision variables. b) Define the objective function Define the constraints d) Determine an optimal solution Problem 3 (points) The network below shows the flows possible between pairs of six locations, Formulate an LP to find the maximal flow possible from Node 1 to Node 6
