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.

Year $123456$

Payments $($$$)87,00096,500104,000119,500141,500171,000$

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

will approve an amount that, along with earnings on investment, will cover the annual 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 $$1,035$ per unit, and the annual coupon rate is $4\mathrm{.}3\%.$ These

bonds mature at the beginning of year $5.$ A maximum of $50$ units may be purchased.

$$ Municipal bonds that may be purchased at the beginning of each year. These bonds mature

in two years and provide a rate of return of $5\mathrm{.}6\%.$ There is no restriction on the amount

placed into these bonds.

$$ A savings account that earns $2\mathrm{.}7\%$ annual interest. There is no restriction on the amount

placed into savings.

Let Z be the total amount invested at the beginning of year $1,$ F be the number of units of federal

bonds purchased at the beginning of year $1,$ Mi be the amount placed into municipal bonds at the

beginning of year i$,$ and Si 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 $($Z$)$ 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$.$