Chapter 5.4, Problem 48E

To determine

To calculate: The number of hours he should spend with each type of client to maximize his income where Slim charges different hourly rates to different categories of individuals $\$5,000$ per hour or private citizens, $\$50,000$ per hour for corporate executives and $\$10,000$ per hour for presidents of universities and he can spend no more than $40$ hours per week in consultation and he feels it would be best if he devoted at least $10$ hours of consultation each week to university presidents and no more half the consultation time is spent with university presidents and at least $2$ more hours of time each week is spent with private citizens than to corporate executives and university presidents combined.