Power over Ethernet systems pass electrical power and data safely on Ethernet cabling.

Question

Power over Ethernet systems pass electrical power and data safely on Ethernet cabling. The function

C(x) = (135+x²)/175x

relates the weekly cost (in thousands of dollars) to a company, to the number x (in hundreds) of PoE systems it manufactures and sells each week. Determine the number of systems the manufacturer must produce to minimize its cost.

Answer 1

The derivative of the cost function is:

C'(x) = -135/(175x²) + x/175

Set the derivative equal to zero and solve for x:

-135/(175x²) + x/175 = 0

x = 11.62

Since x represents the number of systems in hundreds, this means the company should produce approximately 1162 PoE systems per week to minimize costs.

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