1. ## Optimisation problem

Hi, I'm having trouble with this optimisation problem...I hope this is the right place to post this, if not I'm sorry!

"A car travelling at v km/h consumes petrol which costs v^(1/2)/3 cents per km. Find the most economical speed and cost per km if the remaining cost of running the car is 36c an hour."

2. Originally Posted by neobeatlemaniac
Hi, I'm having trouble with this optimisation problem...I hope this is the right place to post this, if not I'm sorry!

"A car travelling at v km/h consumes petrol which costs v^(1/2)/3 cents per km. Find the most economical speed and cost per km if the remaining cost of running the car is 36c an hour."
1. From the speed you see that 1 hour correspond with v km.

2. The total costs are:

$c = \frac13 \sqrt{v}\ \frac{cts}{km} + 36 \frac{cts}{h}$

Now replace hour by v km and you'll get the cost function wrt v:

$c(v)=\frac13 \sqrt{v} \ \frac{cts}{km} + \frac{36}{v} \ \frac{cts}{km}$

3. Differentiate c(v) wrt v and solve for v the equation c'(v) = 0

4. You should come out with $v = 36\ \frac{km}{h}$