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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

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

Grade:Upto college level

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

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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