Stuti is going to franchise a restaurant in the next two years. She wants to open an account at Chase to pay for her expenses. At the beginning of each year, Stuti can make an investment. Any unused money at the start of every year will be deposited into a savings account and earned interest at 2% per year. The below information shows the package Chase offers for Stuti. Immediate reinvestment is possible.

Silver package: Available at the beginning of every year. The matures is 2 years. The return at maturity is 10%.

Gold package: Available at the beginning of year 2 and year 3. The matures is 3 years. The return at maturity is 12%.

Diamond package: Available at year 1. The matures is 5 years. The return at Maturity is 30%.

The expenses are estimated as follows:

Year 1: $12,000

Year 2: $12,000

Year 3: $12,000.

Year 4: $14,000

Year 5: $15,000

Year 6: $18,000

Stuti wants to choose an investment strategy that can generate sufficient funds to cover her expenses for her restaurant with the least amount of initial investment required at the start of the first year. Use this information to formulate a linear programming model.