Libra is planning to start a software company within the next two years. She is considering opening an account with Bank of America to cover his expenses. At the start of each year, Libra can invest some money, and any leftover funds will be deposited into a savings account, earning an annual interest rate of 2%. Bank of America offers the following investment packages with immediate reinvestment:

"Newbie" package: Available at the beginning of every year. It matures in 2 years with a return of 10% at maturity.

"Friend" package: Available at the beginning of year 2 and year 3. It matures in 3 years with a return of 12% at maturity.

"VIP" package: Available in year 1. It matures in 5 years with a return of 30% at maturity.

As estimated, expenses from year 1 - year 3 are $12,000. Then in the last 3 years, it increases by $2,000/year

Libra wants to select an investment strategy that requires the least initial investment at the beginning of the first year while generating enough funds to cover her software company's expenses.

How to formulate this problem as a linear programming mode