Demand, Revenue and Profit Function

Supposeis the unit price a business charges when sellingitems.

If the business sellsitems the total revenue would be

If the cost of producing theitems isthe profit is given by

The aim of the business is to maximise profit. Profit will be maximised when orThis means that profit is maximised when marginal revenue equals marginal cost. To ensure that profit is maximised – and not minimised – we should use the second derivative test. Ifthen profit is maxised.

If the cost functionand price functionthe profit isso and setting this equal to zero gives x=11.94.

so profit is maximised.