# Maximization of Utility Function

Kabir’s utility is $U(c,d,h) = 2c+5d-d2-2h$, where $d$ is the number of hours per day that he spends driving around, $h$ is the number of hours per day spent driving around by the other people in his home town and $c$ is the amount of money he has left to spend on other stuff besides petrol and auto repairs. Petrol and auto repairs cost Rs.$50$ per hour of driving . All the people in Kabir’s home town have the same tastes. If each citizen believes that his own driving will not affect the amount of driving done by the others, they will all drive $D1$ hours per day. If they all drive the same amount,they would all be best off if each drove $D2$ hours per day, where

(a) $D1=2$ and $D2=1$

(b) $D1=D2=2$

(c) $D1=4$ and $D2=2$

(d) $D1=5$ and $D2=0$

I used the formula $$U=2(\bar{M}-50d)+5d-d^{2}-2h$$

and maximized w.r.t $d$ but it's giving an answer: $D1=\frac{5}{102}$

Any help will be appreited.