A serial bond is a type of security that pays off its principal value in regular installments. Dilmohan has $M to invest, and can invest in the following three types of serial bonds:

A $100 serial bond with a maturity of 2 years, priced at $95. A $100 serial bond with a maturity of 4 years, priced at $85. A $100 serial bond with a maturity of 5 years, priced at $80.

For example, buying a serial bond of the first type costs $95, and will pay $50 at the end of this year and at the end of next year.Dilmohan can invest in any number of bonds each year, even fractional values. Any repayments received in a given year can be used immediately for re-investment. Any money that is not invested in serial bonds accrues interest at a rate of 2% per annum. Dilmohan's goal is to maximize the amount of cash he has by the end of year 10. A complicating factor is that at the end of year 10, he does not want to have any money tied up in bonds. For example, he cannot invest in the first type of bond after year 8.

(a) Formulate a Linear Program to help Dilmohan decide on his investment strategy. (b) As part of a scheme to incentivize investment, the government announces a one-time opportunity to loan up to $M in year 3. This loan will need to be paid back by in year 8 with 10% interest (for example, if Dilmohan decides to use this opportunity and takes out a loan of $1000 in year 3, he will need to pay back $1100 in year 8). Adapt your formulation from part (a) to account for this opportunity. (c) Without solving the optimization problem, do you expect Dilmohan to use the loan described in part (b)?