Profit and loss

[kickingtoad]

The marketing research department for a company that manufactures and sells notebook computers established the following revenue and cost functions:

\(\displaystyle {R(x)=60x-2x{2}}\)
\(\displaystyle {C(x)=36x+54}\)

R(x) and C(x) are in millions of dollars.

Break even points are at x=3, 9

Note For parts (B) and (C), since we are talking about production level, the domain of the the profit function, P(x), is [0, infinity)

(B) For what outputs will a profit occur (use interval notation and, if needed, use "infinity" for infinity)?

(C) For what outputs will a loss occur (use interval notation and, if needed, use "infinity" for infinity)

What are the intervals for profit and loss if the Cost equation is a line with different values?

 

[galactus]

Profit is Revenue - Cost

\(\displaystyle 60x-2x^{2}-(36x+54)=-2x^{2}+24x-54\)

For a gain, what values of x make this quadratic > 0

For a loss, what values make it < 0?.

 

[mmm4444bot]

What is your specific question, about this exercise?

I mean, where are you stuck? What have you done, so far?

 

[kickingtoad]

Okay, I got x=3 by using the quadratic formula.

(B) For what outputs will a profit occur (use interval notation and, if needed, use "infinity" for infinity)?

(C) For what outputs will a loss occur (use interval notation and, if needed, use "infinity" for infinity)

How do I write profit and loss as an interval with x=3?

(-infinity,3)...?

 

[mmm4444bot]

Okay, I got x=3 by using the quadratic formula.

That seems like a waste of your time, to me, since they already gave you x = 3 and x = 9 as the inputs leading to the break-even points.


(B) For what outputs will a profit occur (use interval notation and, if needed, use "infinity" for infinity)?

(C) For what outputs will a loss occur (use interval notation and, if needed, use "infinity" for infinity)?

Note that they ask for outputs, not inputs. (The symbol \(\displaystyle x\) is not an output; it's an input.)

The relevant output, in this exercise, is what comes out of the profit function. The symbol used to represent it is given as \(\displaystyle P(x)\).

Are you interpreting the intent of their word "output" to be "input" ? I mean, are you proceeding as if the word "output" is a mistake in the given materials?

OR, perhaps, I'm misinterpreting the word "output" because you have not shared with us the meaning of symbol x. If x is defined in your materials as the number of computers produced by some factory (or something similar), then I suppose we could refer to x as the "factory output", and maybe that's what the instructor is talking about.

I dunno. Could you possibly post the entire exercise?


How do I write profit and loss as an interval with x=3?

This question makes no sense, and I cannot determine what you're actually trying to ask. Please rephrase this question.

Are you taking an on-line math course?