Exercise 5. An investor with $500,000 wants to grow his capital as much as possible over...

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Exercise 5. An investor with $500,000 wants to grow his capital as much as possible over the next 8 years. The following table gives the only types of investment available to him. These investments will also be available at the beginning of each of the next 8 years. # Maximum permitted Type 1 2 3 (inen $000) 100 Unlimited 50 Duration Investment 1 year old 2 years 3 years Performance for the duration 9% 6% 10% Reinvestment Immediate Permitted Permitted Permitted (The return in the table above is as follows: for example, if the investor places $1 at the beginning of the year i in a Type 3 investment, he or she will receive $1.10 at the end of the year. i+2 The maximum allowable of $50,000 applies to the purchase of Type 3 securities at the beginning of a given year; however, it is possible to accumulate Type 3 securities in excess of $50,000, provided they are spread out over more than one year; for example, it would be possible to invest $40,000 in Type 3 at the beginning of each of the first 3 years.) Question 5.1. This exercise can be modelled as a network problem. Give the corresponding graph by specifying the knots and arches. Question 5.2. Give a mathematical model of optimization that would increase the most the capital of the investor. Exercise 5. An investor with $500,000 wants to grow his capital as much as possible over the next 8 years. The following table gives the only types of investment available to him. These investments will also be available at the beginning of each of the next 8 years. # Maximum permitted Type 1 2 3 (inen $000) 100 Unlimited 50 Duration Investment 1 year old 2 years 3 years Performance for the duration 9% 6% 10% Reinvestment Immediate Permitted Permitted Permitted (The return in the table above is as follows: for example, if the investor places $1 at the beginning of the year i in a Type 3 investment, he or she will receive $1.10 at the end of the year. i+2 The maximum allowable of $50,000 applies to the purchase of Type 3 securities at the beginning of a given year; however, it is possible to accumulate Type 3 securities in excess of $50,000, provided they are spread out over more than one year; for example, it would be possible to invest $40,000 in Type 3 at the beginning of each of the first 3 years.) Question 5.1. This exercise can be modelled as a network problem. Give the corresponding graph by specifying the knots and arches. Question 5.2. Give a mathematical model of optimization that would increase the most the capital of the investor.

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