When minimum cost doesn't equal maximum profit

I guess the only time that minimum cost doesn't equal maximum profit is when there are points in the profit function where revenue would increase enough to outweigh the increase in cost. This could occur if there was some sort of additional revenue at a particular point of sales. For instance, if certain customers cost more to service than others, servicing the more profitable customers to a level beyond the point of minimum cost may payoff with additional revenues that make the profit even higher.