Why do businesses want to produce where MC=MR? Explain this idea behind the marginal analysis, and/or give an example of why marginal analysis is necessary to find the profit-maximizing quantity for a business

The best way to analyze choices is marginal analysis. Marginal analysis means looking at the costs and benefits of the "marginal" unit - the next unit, or the additional unit. In the production of a good, the best output level to operate at is where the marginal revenue MR equals the marginal cost MC. Profit will be maximized at that level because to produce one unit beyond the point where MR=MC would mean that the last unit would cost more to produce than it would bring in by generating revenue. On the other hand, producing fewer units than the one where MR=MC would be leaving money on the table because the last unit produced would bring in more marginal revenue than its cost. As an example, think of a widget with a marginal cost of $5 that sells for $5. Since the revenue equals the cost, that widget should be produced because it adds to revenue equal to what it costs to produce. If you go beyond that production, the last widget will cost more than it earns - possibly $5.10.