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girish kumar Grade: Upto college level
        

Dear sir,


Help me solving the below problem.


The cost of fuel for running a train is proportional to the square of the speed in kmph, & costs Rs75 per hour at 17kmph. What is the most economical speed, if the fixed charges are Rs400 per hour


 


Regards


Girish

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear girish


first we should calculate the cost function


C=kv2


put the condition at v=17  ,C= 75


 so k =75/(17)2


so C = 75(v/17)2


now let train has to travel L km


 so time taken by train t =L/v hr


so total cost CT = [75(v/17)2]L/v   +  400 * L/v


                     = 25L [ 3V /172 + 8/V ]


for minimum cost  dCT/dv =0


    this give V = 34√2/√3


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Badiuddin



7 years ago
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