$*$In a construction project, the budget at completion $($BAC$)$ is $$500,000.$ The earned value $($EV$)$ is $$400,000,$ and the actual cost $($AC$)$ is $$450,000.$ What is the Cost Performance Index $($CPI$)?$

a$.$

$1\mathrm{.}11$

b$.$

$1\mathrm{.}25$

c$.$

$0\mathrm{.}90$

d$.$

$0\mathrm{.}80$