A company is about to invest in a joint venture research and development project with another company. The project is expected to last $12$ years, but yearly payments the company makes will begin immediately $($a payment is made today, and the last payment is $12$ years from today$).$ Each payment will be made up of: $1)$ Salaries, which are $$50,000$ every year, and $2)$ Equipment Costs and Facility Overhead, which will start at $$50,000$ and drop by $$5000$ every year until a cost of $$25,000$ is reached, where this cost will remain constant until the end of the project.

a$.$ Draw a cash flow diagram to illustrate the cash flows for this project.

b$.$ At an interest rate of $10\%,$ what is the total future worth of all project

payments at the end of the $12$ years?