according this link: https://en.wikipedia.org/wiki/Financial_cost_of_the_Iraq_War, the direct spending of DoD on Iraq war is about $757.8 billion, do you think most of that spending on the labor?
But consider, the cost of labor effects everything the military does... Everyone in the entire chain commands a higher wage than they would in China/Russia, whether they hold a gun or not... researchers, assembly line workers, doctors, etc... pushing up the costs of everything the military buys.