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Stuck in this problem for quite a while. Anyone can offer some help? The problem is as follows:

Fred has $5000 to invest over the next five years. At the beginning of each year he can invest money in one- or two-year time deposits. The bank pays 4% interest on one-year time deposits and 9 percent (total) on two-year time deposits. In addition, West World Limited will offer three-year certificates starting at the beginning of the second year.These certificates will return 15% (total). If Fred reinvest his money that is available every year, formulate a linear program to show him how to maximize his total cash on hand at the end of the fifth year.

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    I can solve it with brute-force by considering every invest possibility at the beginning of each year. But how to solve it as linear programming? I have trouble in modeling the problem.2011-09-07
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    Is there any cost to 3-year certificate ?2011-09-07
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    I don't think there is. The only condition is the three-year certificate starts at the beginning of the 2nd year.2011-09-07
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    yes but you see the pattern,no?. Is it a compound interest or is the money fixed ? Does it only depend on the money Fred has initially at the beginning of the 2nd year? Then we go for a one year and obtain %4 anyhow, to get the max out of the 3-year thing.2011-09-07
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    My understanding is it's a compound interest. For example, if Fred goes for a one year at the beginning of the first year. then he has 5000(1+4%) available for investment at the beginning of the 2nd year. The problem is he has multiple options in each year. And the available money depends on his previous investments... so I was trapped.2011-09-07
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    I see the difficulty because although it seems like a continuous process this is a discrete time problem. So time is not an issue. it is only a matter of 5 steps that the revenue is maximized in.2011-09-07

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