The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and costs ' 48 per hour at 16 miles per hour. The most economical speed if the fixed charges i.e. salaries etc. amount to 300 per hour is

Step-by-step solution

Let the speed of the train be v and distance to be covered be so that total time taken is s / v hours. Cost of fuel per hour = kv ²( k is constant) Also 48= k .16² by given condition k = 3 16 Cost to fuel per hour 3 16 v ² . Other charges per hour are 300 . Total running cost, array r C= ( 3 16 v ²+300 ) s v = 3 ~s 16 v + 300 ~s v dC dv = 3 ~s 16 - 300 ~s v ² =0 v =40 array d ² C dv ² = 600 ~s v ³ >0 v =40 results in minimum running cost