Solve the Problem $p$ And $x$ , the Quantity of a Certain Product Sold, Obey the Quantity

question 119

Essay

Solve the problem.
-The price $p$ and $x$ , the quantity of a certain product sold, obey the demand equation
$$p = - \frac { 1 } { 10 } x + 100 , \{ x \mid 0 \leq x \leq 1000 \}$$
a) Express the revenue $R$ as a function of $x$ .
b) What is the revenue if 450 units are sold?
c) Graph the revenue function using a graphing utility.
d) What quantity x maximizes revenue? What is the maximum revenue?
e) What price should the company charge to maximize revenue?

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Definitions:

Develop

The process of growth or progression, often involving stages of natural, social, or economic changes and advancements.

Fight-Or-Flight Response

A physiological reaction that occurs in response to a perceived harmful event, attack, or threat to survival, preparing the body to either fight or flee.

Sympathetic Nervous System

A part of the autonomic nervous system that prepares the body for quick action in emergencies; "fight or flight" response.

Hypothalamic-Pituitary-Adrenal

A major part of the neuroendocrine system that controls reactions to stress and regulates many body processes including digestion, immunity, mood, sexuality, and energy usage.