Problem
An investor has $1,000,000 to invest at the start of year 1. He can invest in five different funds A-E. Each fund has different availability and maturity times as shown in the table below. As an example, each dollar invested in fund A at the beginning of year 1 returns $0.50 at the start of year 2 and another $0.80 at the start of year 3. Similarly, each dollar invested in fund B in year 2 yields $1.25 at the start of year 4 (a dash '-' indicates that no money can move in our out of a fund in a given year). Additionally, any money on hand and not placed into an investment at the start of a particular year will earn 8% interest that year. The investor wants to keep at least $50,000 on hand at the start of each year and wants to invest no more than $500,000 in any single fund. Formulate a linear program to enable him to maximize the amount of money on hand at the start of year 4.