Problem $1$

As part of the settlement for a class action lawsuit, Barrick Gold must

provide sufficient cash to make the following annual payments $($in

$$000).$ The annual payments must be made at the beginning of each

year. The judge will approve an amount that, along with earnings on

its investment will cover the annual payments. Investment of the

funds will be limited to savings $($at $2\%$ annually$)$ and $2$ government

securities$.$ Funds not invested in security will be placed in savings.

Securities $1$ and $2$ are available right away but security $3$ will be

available for purchasing at year $3$ and matures after $1$ year. The rates

are based on the PAR value of the security. The plan will be submitted

to the judge and if approved, Barrick will be required to pay a trustee

the amount that will be required to fund the plan. Formulate a model

to help Barrick pay for the settlement with the least amount of funds

pay to the trustee. Solve the model using LINGO. What is the

minimum funds needed? marks