To settle a class action lawsuit related to a data breach involving credit card information, EliteLend

must make cash payments according to the following schedule.

Payments are due at the beginning of each year as indicated. The judge presiding over the case

will approve an amount to be paid now $($i$.$e$.,$ year $0)$ that, along with earnings on investment, will

cover the subsequent payments. The investment options are limited to the following.

Federal bonds with a face value of $$1,000$ per unit that may be purchased only at the beginning

of the plan. The market price is $$1,075$ per unit, and the annual coupon rate is $6\mathrm{.}1\%.$ These

bonds mature at the beginning of year $4.$ A maximum of $40$ units must be purchased.

Municipal bonds that may be purchased at the beginning of each year. These are simple$-$

interest bonds that mature two years from purchase and provide a rate of return of $4\mathrm{.}3\%.$

There is no restriction on the amount placed into these bonds.

A savings account that earns $1\mathrm{.}9\%$ annual interest. To ensure liquidity, this account must

contain at least $$20,000$ at all times.

Let $F$ be the number of units of federal bonds purchased at the beginning of year $0,M_i$ be the

amount placed into municipal bonds at the beginning of year $i,$ and $S_i$ be the amount placed in

savings at the beginning of year $i.$ Develop the linear programming model needed to minimize the

total up$-$front investment that EliteLend will need to make while still ensuring that the provisions

of the court$-$ordered payment schedule are met. Provide all constraints in standard form. You do

not need to solve the $LP.$