A company sells 1000 units of a certain product annually, with no seasonal fluctuations in demand. It always reorders the same number $x$ of units, stocks unsold units until no more remain, and then reorders again. If it costs $b$ dollars to stock one unit for 1 year and there is a fixed cost of $c$ dollars each time the company reorders, how many units should be reordered each time to minimize the total annual cost of reordering and stocking? (Hint:
The company will have an average inventory of $x / 2$ units and must reorder $1000 / x$ times per year. Find the annual stocking and reordering costs and minimize their sum.)