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

question 215

Essay

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?

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Definitions:

Tax

A mandatory monetary fee or different kind of charge levied on a taxpayer by a government entity to support government expenditures and various public costs.

Tax Revenue

The income that is gained by governments through taxation, which is used to fund public services and government obligations.

Tax

A compulsory financial charge imposed by a government on individuals or entities to fund public expenditures, providing revenue for government functions.

Elasticities

Measures in economics that indicate how changes in one variable, such as price or income, affect a change in another variable, such as demand or supply.