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 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 C_T = [75(v/17)²]L/v   +  400 * L/v

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

for minimum cost  dC_T/dv =0

    this give V = 34√2/√3

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