To maximize profit, you need to sell your output at the highest price

To maximize profits a firm need not sell the output at the
highest price. As a matter of fact in most cases trying to increase the price will
result in a loss in revenue and may ultimately lead to a decrease in the profits made.
Selling at the highest price may be possible only in the case of a monopoly or where the
output is an essential product and has very little price elasticity of
demand.

We usually consider a market with perfect
competition for the analysis of the optimum price to be charged and the optimum quantity
to be produced. In perfect competition the price at which the output has to be sold is
its marginal price.

As there is an unlimited demand for the
output, the producer can manufacture as much as it likes but it can sell it only at the
marginal price. The higher the production, the higher are the profits
made.