The cost of running a bus from point A to point B is given by the function: C ( v ) = a v + v b where v is the average speed of the bus in km/h . When the bus travels at 30 km/h , the cost is 75 . W

Question

The cost of running a bus from point A to point B is given by the function: C ( v ) = a v + v b ​ where v is the average speed of the bus in km/h . When the bus travels at 30 km/h , the cost is 75 . When it travels at 40 km/h , the cost is 65 . Determine the most economical speed (in km/h ) for the bus.

TestHub · Accepted Answer

Let cost C = a v + v b ​ According to given question, ​ 30 a + 30 b ​ = 75 40 a + 40 b ​ = 65 ​ On solving (i) and (ii), we get a = 2 1 ​ and b = 1800 Now, C = a v + v b ​ ​ ⇒ d v d C ​ = a − v 2 b ​ d v d C ​ = 0 ⇒ a − v 2 b ​ = 0 ⇒ v = a b ​ ​ = 3600 ​ ⇒ v = 60 kmph ​

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