Due: Wednesday February 6 at the BEGINNING of class
1. Example of a Multiperiod Problem: Investing
A person has $20,000 and plans to invest it over the next 3 years. Their ▯nancial advisor
has suggested three investments to invest in. Each investment can be purchased for
any amount at the beginning of the year and is locked in for one year. The company
the advisor works for has projections for the next 3 years on the rate of return for each
investment. The advisor has also ▯gured out some minimum/maximum levels to invest
in each investment based on the person’s goals and adversion to risk. At the end of
each year, the person can change what they invest in.
investment percent return after one yearInvestment Range
year 1 year 2 year 3
1 4% 5% 6% 9,000-14,000
2 8% 9% 9% 7,000-15,000
3 12% 9% 10% 2,000-5,000
(Note: There is no guarantee that all the money from one year is invested the next
(a) Write a linear program to maximize how much the person is expected to have
after 3 years of investing.
(b) Solve the linear program from part (a) using AMPL. Your solution should in-
clude a prinout of your .mod ▯le that is properly documented to explain your
variables/constraints/what your model is doing, a printout of your .dat ▯le, and
the ▯nal solution including how much the person is expected to have after every
year and how much was invested in each investment every year.
2. Give an example of a linear program