James is planning to invest some money into the bond market in the next 10 years. He has $M to start, and for each year 2 < i < 9, he has an additional $n, to invest. (You should treat M and n, as given constants.) There are 3 types of bonds that he can invest in: • Bond A: Matures in 2 years, pays 4.5% interest each year. Bond B: Matures in 3 years, pays 7% interest each year. Bond C: Matures in 4 years, accumulates 10% interest each year. James can invest in any number of bonds each year. Bonds invested in different years are treated separately, even if they are of the same type. The money invested is locked in, and will be returned to him when the bond matures. For Bonds A and B, the interest is paid to James directly each year. For Bond C, the interest is not paid to James each year. Instead, the interest is added to the amount invested, and paid at maturity. For example, if James invests $100 in Bond A in year i, then he would receive $4.5 in year i +1, $104.5 in year i + 2 (the interest for year i +2 and the original investment), and that is the end of this investment. If he invests $100 in Bond B in year i, then he would receive $7 in years i + 1 and i + 2, and $107 in year i +3. If he invests $100 in Bond C in year i, then he would not get paid any interest in years i +1,i+2, +3. Instead, the value of this bond increases to $110, $121, $133.1 in years i +1,i+2, i + 3 respectively, and it matures with $146.41 returned to him in year i +4. Money from any interest paid or any matured investment can be used to invest in more bonds in the same year, if he chooses to do so. All invested bonds must mature by year 10, e.g, the latest that Bond C can be invested is year 6, which matures during year 10. Any money that James has that is not invested into bonds is put into a savings account, which will earn 2.5% interest every year. Formulate a linear program that would decide how James should invest his money, maximiz- ing the total amount of money James would have at year 10.