Question
The receipts on railway travel vary as the excess of speed of the train over 30 kmph. The expenses vary as the square of that excess. What is the speed at which the profits will be greatest if at 60 kmph is the expenses are just covered?
Answer: Option C
:
C
Option(c)
Let the excess of speed over 30 kmph=S
Receipts= R and Expenses=E
Then
R=K1 S
And E= K2S2
Also, at 60kmph, R=E
Thus, K1=30 K2
We need to maximize R-E= K1S- K2S2
=SK2(30-S)
S+30-S, the sum is constant, the product will be maximum when they are equal
Thus S=30-S → S=15. Speed = 30+15= 45
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:
C
Option(c)
Let the excess of speed over 30 kmph=S
Receipts= R and Expenses=E
Then
R=K1 S
And E= K2S2
Also, at 60kmph, R=E
Thus, K1=30 K2
We need to maximize R-E= K1S- K2S2
=SK2(30-S)
S+30-S, the sum is constant, the product will be maximum when they are equal
Thus S=30-S → S=15. Speed = 30+15= 45
Was this answer helpful ?
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