Alexis is in the first year of her undergraduate program. Her father has contributed £25,000 toward her education. From this amount she must pay her tuition for the first three years and she expects a tuition waiver for the fourth year. Since she wants to pursue her master's after four years, she wants to invest the funds in a bank in different instruments and to maximize her return at the end of the 4th year. She is considering four investment options over the next four years: Type A, a 1-year investment that yields 6% percent interest on the principle; Type B, a 2-year investment that yields 14% interest on the principle; Type C, a 3-year investment that yields 22% interest on the principle; Type D, a 4-year investment that yields 28% interest on the principle. For example, if she invests a principle of £100 today in Type B, at the end of second year, she will get an interest of 14% (i.e., £14) along with her principle amount of £100, totaling to £114. Notice that the interest rate is not on yearly basis but based on the whole period of investment. 

She pays a tuition fee of £3,000 in the first year, £2,000 in the second year, and £3,000 in the third year. The amount invested in Type B starting from Year 2 is to be at most 20% of total amount invested in the starting of Year 2. At the end of the fourth year, Alexis wants to have maximum returns consisting of principle plus interest from her investments.
a. Formulate a linear programming model.
b. Solve the model by using the computer.