SKILL CHECK

John has $$20,000$ to invest in three funds F$1,$ F$2$ and F$3.$ Fund F$1$ offers a return of $2\%$ and has a low risk. Fund $F2$ offers a return of $5\%$ and has a medium risk. Fund $F3$ offers a return of $10\%$ but has a high risk. To be on the safe side, John wants to invest no more than $$3000$ in F$3$ and at least twice as much in F$1$ as in F$2.$ Assuming that the rates hold until the end of the year, what amounts should he invest in each fund in order to maximize the year end return?

Construct a linear program which models this problem.