The roots of the quadratic function describing the relationship between number of products produced and overall profit margin are x=0 and 36. The vertex is a minimum at (18,−35). The company actually loses money on their first few products as it costs them more to make them, but once they hit items they break even again. The worst case scenario is that they produce items, as they will have a profit of
dollars.

The first root tells us that the profit will be 0 when products are sold.