Problem $5$: An investor would like to determine how to allocate $$1000$ among four investments. Based

on forecasts from market analysts, the return per dollar invested in each investment can be

characterized into three scenarios. These returns are given in the following table:

The investor would like to invest conservatively, so as to maximize the minimum return produced

among the three scenarios. To limit transaction fees, the investor would like to allocate money to no

more than three of the four investments.

Part a: Formulate an integer$-$linear programming model for this problem.

Part b: Solve the problem using AMPL$/$CPLEX and report the obtained optimal solution. Include a typed

version of your AMPL model file and$/$or data file and your AMPL session in your submission.