Consider a transit line of length L with n equally spaced stations and a terminal. The first of the n stations (n = 1) lies at one end of the line; the terminal lies at the opposite end.
The daily cost of providing transit service is C1/x + C2x2 ($/day), where constants C1, C2 > 0 and x is the distance between each station; (x is also the distance between the terminal and station number n).
Determine n*, the number of transit stations (excluding the terminal) that minimizes total cost per day. Write the expression for n* in terms of the variables given