Science:Math Exam Resources/Courses/MATH102/December 2016/Question B 07 (c)
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Question B 07 (c) 

Each day 100,000 people use Vancouver’s public transit system. Translink estimates that 2000 of those people ride on transit without paying (called free riders). The number of free riders caught by Translink officers in any particular day is given by where and is the number of Translink officers on duty that day. Each officer on duty costs Translink 1000 dollars per day. (c) For what value of , the fine, is it optimal to hire exactly one officer? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
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Hint 

From the part (b), it is enough to find such that . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. From the Hint, we find such that . By some simple computation, we get
Therefore, the optimal fine is 