maths question ......?

Question

7)A power unit is there by the bank of the river of 900 mtr width. a cable is made from power unit to power a plant opposite to that of the river and 3000 mtr away from the power unit. The cost of the cable bellows water Rs5 / mtr and cost of cable on the bank is Rs 4/ mtr. Find the pt where the cable cut through the river.

Answer 1

The question is not quite clear to me, but I tried to interpret it somehow. According my interpretation of the question I cooked this solution.

Let
x - be the distance of the point where the cable cut through the river from the point on riverside just opposite of the power unit (this is the distance to be find)

Solution:

The cost of the cable is:

y = 5 * (900^2 + x^2)^0.5 + 4*(3000 - x)

Minimum of this function is to be find.

y' = 0

5 * 0.5 * (900^2 + x^2)^(-0.5) * 2 + 4 * (-1) = 0

Try to solve this equation, I am lazy to do it.
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