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:

Critical Problems

significant, urgent issues or challenges that require immediate attention and resolution to prevent adverse outcomes.

Certainty

The state of being completely confident or having an absolute conviction about something, without doubt.

Risk and Uncertainty

Refers to situations where the outcomes or consequences of actions are unknown, with risk implying some knowledge of probability and uncertainty indicating a complete lack of predictability.

Personal Judgments

Opinions or decisions formed by individuals based on personal feelings, tastes, or opinions, often without external input or influence.