Explain why a profit-maximizing monopolist would never choose to operate on the inelastic portion of its demand curve

This question appears at first as counter-intuitive as one might imagine that where demand is inelastic and consumers are not responsive to a rise in price, this would be ideal for a monopoly to make a profit. However, profit maximizing has little do with individual consumer responsiveness, but the overall market. As we know profit is maximized where the Marginal Cost (incremental cost) is equal to the Marginal Revenue (incremental revenue), which is at a positive intersect on the elastic region of the demand curve, which achieves a higher price than on the inelastic region, with less output (less production costs), resulting in a greater profit for the monopolist. In terms of revenue, the monopoly will also always operate where the Marginal Revenue(MR) curve is positive to ensure an optimal total revenue. The region in which the MR curve is positive is always demand elastic.                                                                                                              Overall, the key points are: -> Profit maximizing output is determined by MC and MR intersect not elasticity ->Inelastic region of the demand curve is associated with lower prices and greater quantities that would not maximize profit ->Profit maximizing occurs in the region where MR is positive.  Note: during a session a monopoly graph would be shown with points,curves and regions on display