A bakery works out a demand function for its chocolate chip cookies and finds it to be $q=D(x)=711-22 x$, where $q$ is the quantity of cookies sold when the price per cookie, in cents, is $x$. Use this information to answer parts a) through $\mathrm{f}$ ).
a) Find the elasticity.
\[
E(x)=\frac{22 x}{711-22 x}
\]
b) At what price is the elasticity of demand equal to 1 ?
(Round to the nearest cent as needed.)
Answer
Final Answer: The price at which the elasticity of demand is equal to 1 is \(\boxed{16.16}\) cents.
Step 1 ：The elasticity function is given by \(E(x)=\frac{22 x}{711-22 x}\).
Step 2 ：To find the price at which the elasticity of demand is equal to 1, we need to solve the equation \(E(x)=1\) for \(x\). This gives us the equation \(\frac{22 x}{711-22 x}=1\).
Step 3 ：Solving this equation gives us \(x = \frac{711}{44}\).
Step 4 ：However, the question asks for the answer to be rounded to the nearest cent. So, we round \(x\) to get the final price.
Step 5 ：Final Answer: The price at which the elasticity of demand is equal to 1 is \(\boxed{16.16}\) cents.
