Francois and Camille Merrit recently inherited a substantial amount of money from a deceased relative. They want to use part of this money to establish an account to pay for their daughter$$s college education. Their daughter, Lisa, will be starting college five years from now. The Merrits estimate that her first year college expenses will amount to $$12,000$ and increase $$2,000$ per year during each of the remaining three years of her education. The following investments are available to the Merrits:

Investment Available Matures Return at Maturity

A every year $1$ year $6\%$

B $1,3,5,72$ years $14\%$

C $1,43$ years $18\%$

D $17$ years $65\%$

The Merrits want to determine an investment plan that will provide the necessary funds to cover Lisa$$s anticipated college expenses with the smallest initial investment.

a$)$ Formulate an LP model for this problem.

b$)$ Create a spreadsheet model for this problem and solve it using Solver.

c$)$ What is the optimal solution?