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:

ERG Theory

ERG Theory is a motivational theory developed by Clayton P. Alderfer that categorizes human needs into three basic levels: Existence, Relatedness, and Growth, suggesting that these needs can be pursued simultaneously.

Alderfer

A psychologist known for developing the ERG (Existence, Relatedness, and Growth) theory as an extension of Maslow's hierarchy of needs.

Psychological Growth

The development of an individual’s emotional and cognitive capabilities and their capacity for adaptive behavior and understanding.

Interpersonal Relationships

The connections and interactions between two or more people, which can affect both personal and professional contexts significantly.