Yokam Company is considering two alternative projects. Project $1$ requires an initial investment of $$590,000$ and has a present value of all its cash flows of $$1,150,000.$ Project $2$ requires an initial investment of $$5$ million and has a present value of all its cash flows of $$7$ million.

$($a$)$ Compute the profitability index for each project.

$($b$)$ Based on the profitability index, which project should the company select?