The CTC phone company is a regional supplier of long-distance telephone services. CTC is trying to determine the optimal pricing structure for its daytime and evening long-distance calling rates. The daytime price applies from 8AM to 6PM and the evening price applies the rest of the time. With the help of a consultant, CTC has estimated the average demand for phone lines as follows:
D = 6?00 5000+P 300P DE
E = 40+0 600P? 2500P DE
We denote by D the hourly demand for daytime phone lines, by E the hourly demand for evening phone lines, by PD the day price, and by PE the evening price.
Determine the maximal revenue that CTC can expect and the prices (day and evening) that generate the maximal revenue.