Given the following information for a six$-$month project:

Planned Value $(PV)=$$$50,000$

Earned Value $(EV)=$$$60,000$

Actual Cost $(AC)=$$$45,000$

Budget $At$ Completion $(BAC)=$$$100,000$

a$.$ Find the cost variance $($CV$),$ schedule variance $($SV$),$ cost performance index $($CPI$),$ and schedule performance index $($SPI$)$ for the project.

b$.$ Use your answer in part $($a$)$ to evaluate the project development. Is it ahead of schedule or behind schedule? Is it under budget or over budget?

c$.$ Use the CPI to calculate the estimate at completion $($EAC$)$ for this project. Is the project performing better or worse than planned?

d$.$ Use the SPI to estimate how long it will take to finish this project if the original duration of the project is $6$ months.