Profit (in dollars) for a company when x units of a certain product are produced is given by $P ( x ) = ( 100 - x ) \ln x$ when x 1.(a) What is the marginal profit (the derivative of the profit function)?
(b) If the current production level is x = 15, is the profit increasing or decreasing?
(c) If the current production level is x = 40, is the profit increasing or decreasing?
(d) At approximately what production level does the profit function reach its maximum value? What is the maximum profit?

Question

Profit (in dollars) for a company when x units of a certain product are produced is given by $P ( x ) = ( 100 - x ) \ln x$ when x > 1.(a) What is the marginal profit (the derivative of the profit function)?
(b) If the current production level is x = 15, is the profit increasing or decreasing?
(c) If the current production level is x = 40, is the profit increasing or decreasing?
(d) At approximately what production level does the profit function reach its maximum value? What is the maximum profit?

Quizplus · Accepted Answer

The Answer of Profit (in dollars) for a company when x units of a certain product are produced is given by $P ( x ) = ( 100 - x ) \ln x$ when x > 1.(a) What is the marginal profit (the derivative of the profit function)?
(b) If the current production level is x = 15, is the profit increasing or decreasing?
(c) If the current production level is x = 40, is the profit increasing or decreasing?
(d) At approximately what production level does the profit function reach its maximum value? What is the maximum profit?

Profit (In Dollars) for a Company When X Units of a Certain