Chapter 2.5, Problem 91E

5 Use a spreadsheet to numerically verify the result of Exercises 1-55.

For Exercises 23-28 find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit, Assume that revenue, $\text{R}\left(\text{x}\right),and\cos t,\text{C}\left(\text{x}\right),areindollarsfor$

Exercises 23-26

Vanity license plates. According to a pricing model, increasing the fee for vanity license plates by $1 decreases the percentage of a state’s population that will request them by 0.04% (Source: E. D. Craft, “The demand for vanity (plates): Elasticities, net revenue maximization, and deadweight loss, “ Contemporary Economic Policy, $Vol,20,133-144\left(2002\right)$

)

a. Recently, the tee for vanity license plates in Maryland was $25, and the percentage of the state’s population that had vanity plates was 2 13% Use this information to construct the demand function, $q\left(x\right)$, for the percentage of Maryland’s population that will request vanity license plates for a fee of x dollars.

b. Find the fee, x, that will maximize revenue from vanity plates