Answers

2015-04-15T19:03:49+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
 rate of cost of fuel FC =  price of fuel  P *  volume of fuel consumed V
    
rate of cost of fuel FC is proportional to the square of speed.    So  volume V of fuel consumed per hour is proportional to the square of speed v  in kmph.

  rate of fuel cost FC = $ 64 /hour        for Speed v = 16 kmph
                 FC = K v²            , where K is the constant of proportionality.
          => $ 64 = K * 16²    =>  K = 0.25 $-Hr/km²

  rate of other costs OC =  $ 100 / hour

 total costs rate = TC = FC + OC = 0.25 v²  + 100      $ / hour

 Let the engine in the vehicle drive the vehicle for a distance of  S km.  Then the time taken to cover the distance S is :  T = S / v.    The total distance S to be travelled is a constant.
 
  Total cost for  T hours in $
     C   =  T * (0.25 v² + 100) 
          =  S / v * (0.25 v² + 100)
          = 0.25 S  v  + 100 S / v
 
differentiate C wrt   v  and find the value of v for which  C is minimum.

  d C / d v =  0.25 S - 100 S / v²
                     = 0    for minimum
           so  0.25 = 100 / v²
                 v² =  400
                   v = 20 kmph
===========
So the minimum cost of running the engine is :   0.25 *  20² + 100 = 200 $ / hour


1 5 1