If C(x) = 0.001x² + 1000 dollars is the cumulative cost of running the Acme factory, we can find the cumulative profit of the Acme factory by subtracting the cumulative cost from the total revenue. Let's assume that the total revenue is a constant value of R dollars.
Therefore, the cumulative profit function P(x) can be written as:
P(x) = R - C(x)
Where R is the total revenue and x is the number of days since the start of 2018. The unit of the function's output will be dollars, since both the total revenue and the cumulative cost are measured in dollars.
Therefore, P(x) = R - (0.001x² + 1000) dollars
It is important to note that the value of R is not given in the problem statement and it is unknown, thus the function P(x) is not complete without the value of R. In addition, a proper function would have the start date of the factory and the end date, but it's mentioned to be since the start of 2018.