Chapter 5.2, Problem 55E

Research and Development Spending on research and development by drug companies in the United States t years after 1970 can be modeled by

$S\left(t\right)=2.5e^{0.08t}\text{ billion dollars }\left(0\le t\le 31\right).$

The number of new drugs approved by the Food and Drug Administration (FDA) over the same period can be modeled by

$D\left(2\right)=10+t\text{ drugs per year }\left(0\le t\le 31\right).$

When was the function $D\left(t\right)S\left(t\right)$ ata maximum? What is the maximum value of $D\left(t\right)S\left(t\right)$? What does the answer tell you about the cost of developing new drugs?