Why this answer
The project has completed 40% of the work, so the earned value (EV) is 40% of the total budget. With actual cost (AC) of $500,000 and planned value (PV) of $450,000, the CPI = EV/AC = (0.4 * BAC)/500,000. Since AC > PV and EV < PV (because only 40% of work is done vs. 45% planned), both CPI and SPI are less than 1.0, indicating the project is over budget and behind schedule.
How to eliminate wrong answers
Option A is wrong because being over budget (CPI < 1) does not automatically mean ahead of schedule; SPI must be > 1 for that, but here EV ($400,000 if BAC = $1,000,000) is less than PV ($450,000), so SPI < 1, meaning behind schedule. Option B is wrong because both CPI and SPI would need to equal 1.0, but AC ($500,000) exceeds EV ($400,000) and EV is less than PV ($450,000), so neither index is 1.0. Option C is wrong because under budget requires CPI > 1 (EV > AC), but here EV ($400,000) is less than AC ($500,000), so CPI < 1, and ahead of schedule requires SPI > 1, but EV ($400,000) is less than PV ($450,000), so SPI < 1.