Let R(x) be the revenue obtained from the production and sale of x units of a commodity,

Question:

Let R(x) be the revenue obtained from the production and sale of x units of a commodity, and let C(x) be the total cost of producing the x units. Show that the ratio

is optimized when the relative rate of change of revenue equals the relative rate of change of cost. Would you expect this optimum to be a maximum or a minimum?

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