Solve
-A Specialty Watch Company's Monthly Profit Equation Is $$P = - 2 x ^ { 2 } + 1000 x + 50,000 \text {, }$$

Solve.
-A specialty watch company's monthly profit equation is
$$P = - 2 x ^ { 2 } + 1000 x + 50,000 \text {, }$$
where $x$ is the number of watches manufactured. Find the maximum monthly profit and the number of watches must be produced each month to attain the maximum profit.

A) Maximum profit $= \$ 50,000$
number of watches produced $= 1000$
B) Maximum profit $= \$ 175,000$
number of watches produced $= 250$
C) Maximum profit $= \$ 175,000$
number of watches produced $= 500$
D) Maximum profit $= \$ 50,000$
number of watches produced $= 0$