Chapter 3.3, Problem 81E

Profit A company that produces calculators estimates that the profit $$P$$(in dollars) from selling a specific model of calculator is given by

$$P=–152x^3+7545x^2–169,625,0\le x\le 45$$

where $$x$$is the advertising expense (in tens of thousands of dollars).For this model of calculator, an advertising expense of $$\text{\$}400,000$$ $$(x=40)$$results in a profit of $$\text{\$}2,174,375.$$

(a) Use a graphing utility to graph the profit function.

(b) Use the graph from part (a) to estimate another amount the company can spend on advertising that results in the same profit.

(c) Use synthetic division to confirm the result of part (b) algebraically.