To settle a class action lawsuit related to a medical records data breach, CareSync must make cash payments according to the following schedule. The annual payments must be made at the beginning of each year. The judge in the lawsuit will approve an amount that, along with earnings on investment, will cover the annual payments. The investment options are limited to the following. - Federal government 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 $1,025 per unit, and the annual coupon rate is 4.8%. The bonds mature at the beginning of year 5 . No more than 250 units of the bond may be purchased. - Municipal annunities that may be purchased at the beginning of each year. These annuities mature in two years and provide a rate of return of 7.4%. There is no restriction on the amount placed into annuities. - A savings account that earns 3.1% 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 units of federal bonds purchased at the beginning of year 1,Mi be the amount placed into annuities 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 CareSync 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