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:

Environmental Resistance

Factors in the environment that limit the growth, abundance, or distribution of organisms or populations.

Intraspecific Competition

A form of competition where individuals of the same species compete for the same resources in an ecosystem, such as food, space, or mates.

Uniform Dispersion

A distribution pattern where individuals of a particular species are evenly spread out across a habitat or area, minimizing competition and maximizing resource use.

Interspecific Predation

The predation that occurs when a member of one species hunts and consumes a member of another species.