why is the profit maximising output where marginal cost (MC)= marginal revenue (MR)?

Marginal revenue is the revenue generated by selling the last unit of output. Marginal cost is the cost of producing the last unit of output. Profit is maximised at the output where MC=MR because if less output is produced, MR will be higher than MC, and so if output was increased to where MC=MR, more revenue would be made from selling the additional output than the cost of producing these units of output and so more profit is made. If the level of output produced was greater than where MC=MR, MC is greater than MR, and so the cost of producing the units of output above the profit maximising level is greater than the revenue generated from those units of output, and so less profit is made. Because of this profit is maximised when MC=MR.