Chapter 8.1, Problem 41HP

To determine

To find: The price to deliver the maximum dollar sales.

Explanation of Solution

Given information:

The number of students attend the fall dance if tickets cost $\$30$ each is $100$ and if each $\$5$ increased in the price, $10$ fewer students will attend.

The equation for the total price of the sale is obtained as,

  $y=\left(100-10x\right)\left(30+5x\right)$

Case 1: if $x=0$ ,

  $\begin{array}{c}y=\left(100-10\times 0\right)\left(30+5\times 0\right)\\ =\$3000\end{array}$

Case 2: if $x=1$ ,

  $\begin{array}{c}y=\left(100-10\times 1\right)\left(30+5\times 1\right)\\ =90\times 35\\ =\$3150\end{array}$

Case 3: if $x=2$ ,

  $\begin{array}{c}y=\left(100-10\times 2\right)\left(30+5\times 2\right)\\ =80\times 40\\ =\$3200\end{array}$

Case 4: if $x=3$ ,

  $\begin{array}{c}y=\left(100-10\times 3\right)\left(30+5\times 3\right)\\ =70\times 45\\ =\$3150\end{array}$

From the above calculation, the maximum dollar sales obtained at $\$40$.

Thus, the correct option is $\text{H}$.