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January 25th, 2011, 05:59 PM   #1
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Op. Res: What next?

Operations Research Questions: You have $5000 to invest for five years. At the beginning of each year, you can invest in one- or two-year bond at 4% and 9% total interest, respectively. At the start of the second year, you can invest in three-year 15% total interest bond. Find a linear program to maximize total cash after five years.

My answer (so far):
: amount available to invest end of year i ($); i=0,1,2,3,4,5
: amount invested at end of year i in j-length bonds ($); i=0,1,2,3,4; j=1,2,3

ex: x_{0,1} is the amount invested at the end of year 0 (beginning of year 1) in 1-year bonds

Objective: Maximize .

Constraints:


The amount of money available at end of year i equals the amount of money invested in 1-, 2-, and 3- year bonds at the end of year i:


The amount of money available at end of year i equals the amount of money rolling off investments from 1, 2, and 3 years earlier:


Equate the s (and rearrange a little bit):



So what's next? I have 5 equations and 15 unknowns. I've tried thinking of ways to substitute to reduce variables, but can't find any. My classmate says it's five equations and five unkowns.

TIA.
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