This rearrangement shows that when x=79/0.4, R(x) has a maximum value of 0.2(79/0.4)²=7801.25.
However, x=79/0.4=197.5 wrist watches. R(197)=R(198)=7801.20. The sale of 197 or 198 watches raises 7801.20 in revenue.
(b) P(x)=R(x)-C(x)=79x-0.2x²-32x-1650=47x-0.2x²-1650 is the profit function.
(c) To maximise profit x=47/0.4=117.5, so P(117)=P(118)=1111.20. 117 or 118 watches need to be sold.
(d) (a) doesn’t take into account the cost of making the watches. A quadratic function provides a target for the vender and allows the firm to plan production more efficiently. Also, it is easier to work out the target when a quadratic function applies. A linear equation cannot fix a target, because profit just increases with sales. More complex functions (polynomials with higher degree than 2) are more difficult to solve to find targets, and may generate more than one target.