Profit maximization is: given a set of "demand points", each with quantity demanded and maximum acceptable price, adjust the price level such that the maximum profit (revenue, actually, so far) is attained. A lower price might capture more of the market segment and thus get a greater quantity, but it will be multiplied by a lower price. A higher price might get less of the market but it will get a greater return per quantity. Kind of like intersecting supply and demand. But it tries all combinations.
The inverse utility function is used to calculate the maximum price that would be acceptable to a demander. Assuming it is a physical resource, it is a trade-off between price and distance; a different supplier might be just as acceptable as another (equal utility rating) depending on its price and distance. To steal a customer from a competitor, your building's utility rating has to be greater. This leads to price competition as different AI's keep lowering their prices until they reach the lowest profitable price or reach their building's production capacity.
So far there's no lower limit on price that would be due to cost of inputs and operation.