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Problem 1. [12 points] 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.
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I know how to set up the problem and I know I have to take the first derivative and set it equal to 0. However I'm not sure how. Can you explain how to solve this? Thanks
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