Question 5 (10 points) An investor who has 500,000 dollars wants to grow as much as possible its capital over the next 4 years. The following table gives the only types of investments available to him. These investments will also be offered at beginning of each of the next 4 years. Type Duration of investment Yield for the duration Reinvestment immediate Maximum permits (in 000 Dollars) 90 unlimited WN 1 2 3 1 year 2 years 3 years 8% 7% 9% permit permit Permit 50 (The performance in the table above is interpreted as follows: for example, if the investor places $1 at the beginning of year i in a Type 3 investment, he will receive $1.10 $ at the end of year i+2. The maximum allowed of $50,000 applies to the purchase of securities of type 3 at the beginning of a given year; however, it is possible to accumulate securities type 3 over $50,000, provided they spread their purchase over more than one year: for example, it would be allowed to invest $ 80,000 in type 1 at the beginning of each of the first 3 years.) Question 5.1. (10 pts.) Our goal is to model this exercise as a network problem. Give the corresponding network graph by specifying the nodes, arcs, capacity of arcs and yields (%) associated with arcs. (Do not give the mathematical model.) Question 5 (10 points) An investor who has 500,000 dollars wants to grow as much as possible its capital over the next 4 years. The following table gives the only types of investments available to him. These investments will also be offered at beginning of each of the next 4 years. Type Duration of investment Yield for the duration Reinvestment immediate Maximum permits (in 000 Dollars) 90 unlimited WN 1 2 3 1 year 2 years 3 years 8% 7% 9% permit permit Permit 50 (The performance in the table above is interpreted as follows: for example, if the investor places $1 at the beginning of year i in a Type 3 investment, he will receive $1.10 $ at the end of year i+2. The maximum allowed of $50,000 applies to the purchase of securities of type 3 at the beginning of a given year; however, it is possible to accumulate securities type 3 over $50,000, provided they spread their purchase over more than one year: for example, it would be allowed to invest $ 80,000 in type 1 at the beginning of each of the first 3 years.) Question 5.1. (10 pts.) Our goal is to model this exercise as a network problem. Give the corresponding network graph by specifying the nodes, arcs, capacity of arcs and yields (%) associated with arcs. (Do not give the mathematical model.)
