Today is Dec $31,$ Year $0.$ You have been asked to manage $$380,000$ for Mrs$.$ C$.$

Investment opportunities: There are two bonds which are appropriate for Mrs$.$ C$.$ Bond A matures

on Dec $31,$ Year $1$ and offers $4\%$ per annum. Bond B matures on Dec $31,$ Year $2$ and offers $7\%$ per annum. All interest are paid out at the end of each year on Dec $31.$ You can purchase the bonds in any amount today, but you cannot short the bonds and you cannot purchase them at a later date. In addition, spare cash can be held in a savings account which offers $1\%$ interest per annum, including at the end of Year $2.$

Expenses: Her son is going to university next year, and she wants to give him some money on Dec $31,$ Year $1$ and Dec $31,$ Year $2.$ She has not decided the exact amount that she will give him on each date. He will need at least $$175,000$ per year, and she wants to give him $$425,000$ in total. She wants to give him approximately the same amount each year, so she asks you to minimize the difference between the two gifts.

Line of credit: Mrs$.$ C has a line of credit that allows her to borrow at most $$100,000.$ She can take out money on her line of credit on Dec $31$ of Year $0$ or Year $1.$ Interest on the outstanding debt is payable at $3\%$ per annum at the end of each year. She can repay parts or all of the principle on Dec $31$ of each year. She wants to be debt$-$free on Dec $31,$ Year $2.$

a$)$ Write a linear program to determine how Mrs$.$ C should invest her money and$/$or borrow funds in order to fund her son$$s education expenses over the next two years.

Do NOT argue for$/$against any investment decisions before setting up your LP$.$ Your LP should be able to identify sub$-$optimal strategies. You may only assume that you will not keep cash on hand today.

b$)$ Use Gurobi in Python to solve your LP$.$ Submit your code.

c$)$ Using your solution from part b$,$ what investment advice will you give Mrs$.$ C$?$ State her investments, borrowed funds, interest revenue, and interest expense at the end of each year. Also state the amounts that she should give her son on Dec $31,$ Year $1$ and Dec $31,$ Year $2.$