Solve the Problem $P ( x )$ For a Company Producing $x$

question 263

Multiple Choice

Solve the problem.
-The total profit function $P ( x )$ for a company producing $x$ thousand units is given by $P ( x ) = - 2 x ^ { 2 } + 30 x - 100$ . Find the values of $x$ for which the company makes a profit. [Hint: The company makes a profit when $\mathrm { P } ( \mathrm { x } ) > 0$ .]

• A) \(x\) is between 5 thousand units and 10 thousand units
• B) \(x\) is greater than 5 thousand units
• C) \(x\) is less than 10 thousand units
• D) \(x\) is less than 5 thousand units or greater than 10 thousand units

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Definitions:

Bud Scale Scars

Marks left on a twig after bud scales (which protect the bud during winter) fall off in the spring, indicating where new growth began.

Haustoria

Specialized structures of parasitic or symbiotic fungi and plants that penetrate the host's tissue to absorb nutrients.

Adventitious

Referring to structures that develop in an unusual place, such as roots growing from stems or leaves instead of from the plant's root system.

Taproots

A type of root system characterized by a single, large, central root that grows vertically downward and gives off smaller lateral roots.