# Science:Math Exam Resources/Courses/MATH102/December 2016/Question B 07 (c)/Solution 1

From the Hint, we find such that .

By some simple computation, we get

Therefore, the optimal fine is

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From the Hint, we find $F\geq 250$ such that $N_{0}=500\ln \left({\frac {F}{250}}\right)=1$.

By some simple computation, we get

$500\ln \left({\frac {F}{250}}\right)=1\iff \ln \left({\frac {F}{250}}\right)={\frac {1}{500}}\iff {\frac {F}{250}}=e^{\frac {1}{500}}\iff F=250e^{\frac {1}{500}}$

Therefore, the optimal fine is $\color {blue}F=250e^{\frac {1}{500}}(dollars)$

- This page was last edited on 15 December 2017, at 05:36.