Chapter 3.3, Problem 90E

HOW DO YOU SEE IT? The graph below shows a company’s estimated profits for different advertising expenses. The company’s actual profit was $$\text{\$}936,660$$for an advertising expense of $$\text{\$}300,000.$$

(a) From the graph, it appears that the company could have obtained the same profit for a lesser advertising expense. Use the graph to estimate this expense.

(b) The company’s model is

$$P=–140.75x^3+5348.3x^2–76,560,0\le x\le 35$$

where $$P$$is the profit (in dollars) and $$x$$is the advertising expense (in tens of thousands of dollars).Explain how you could verify the lesser expense from part (a) algebraically.