Exercise 55 Page 287

Let's follow the graphical approach and use a calculator to find the $x\text{-}$intercepts of the graph. From the screen with your graph, push $\boxed{\text{2nd}}$ and $\boxed{\text{TRACE}}$ and choose zero from the menu. The calculator will prompt you to choose a left and right bound and to provide the calculator with a best guess of where the zero might be. The results we obtained give bounds for the possible values of $x$ satisfying the inequality of Part A. If we round these bounds to the nearest integer, this means that the manufacturer must sell between $30$ and $98$ thousand digital audio players to earn a profit of at least $\$100000$ in a month.

This subtraction represents a translation down $25000$ units of the graph of the profit function. This shift also applies to the inequality we need to solve when looking for quantities to sell to reach $\$100000$ profit. This reduces the interval where the manufacturer can reach at least $\$100000$ profit.

We can use the calculator again to find the $x\text{-}$intercepts of the new graph.

The results we obtained give bounds for the possible values of $x$ satisfying the new inequality. If we round these bounds to the nearest integer, with the increased expenses the manufacturer must sell between $47$ and $81$ thousand digital audio players to earn a profit of at least $\$100000$ in a month.