Marginal revenue problem: R = 2x(900 + 32x - x^2)

A

AGlas9837

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I have answers for this problem, but don't know if they are correct:

The revenue (in dollars) from renting x apartments can be modeled by

R = 2x(900 + 32x - x^2).

a) Find the additional revenue when the number of rentals is increased from 14 to 15.

Here, I substituted 14 and 15 into the original equation:

so for 14, I get 2(14)(900 + 32(14) - 14^2) = 32,256
and for 15, 2(15)(900 + 32(15) - 15^2) = 34,650

b) Find the marginal revenue when x = 14. Here, I took the derivative, 2(32 - 2x), and substituted with 14:

2(32 - 30) = 4

c) Compare the results of parts (a) and (b). I expected the numbers would at least be similar here but they are not even close so I'm pretty sure my answers are incorrect. What have I done wrong here?
 
AGlas9837 said:
R = 2x(900 + 32x - x^2).
Click to expand...
My very first impression of this equation was that you had used 'x' to mean multiplication and to mean your independent variable.

Second, when you evaluated R(14) and R(15), clearly this was not the case.

Third, when you decided to find the derivative, you entirely ignored the first 'x', possibly indicating that my first impression was correct.

So, which is it?

R(x) = 2x(900 + 32x - x^2) = 1800x + 64x^2 - 2x^3

or

R(x) = 2(900 + 32x - x^2) = 1800 + 64x - 2x^2

Important Rule: Never, ever use 'x' to mean multiplication, no matter how many times you have seen it written like that.
 
Okay, then the derivative is no good. Try that again.
 
I'm at a complete loss! The derivative of 2x is 2. The derivative of 900 is 0. The derivative of 32x is 32 and the derivative of x^2 is 2x so I don't know what else it could be! I've looked at other similar problems and I don't understand why what I've got isn't correct.
 
AGlas9837 said:
I'm at a complete loss!
Click to expand...
You might want to review the Product Rule, or else multiply out the original function before attempting the derivative. :wink:

Eliz.
 
I just don't understand the calculus requirements in a course where calculus is not a prerequisite. You must have the required tools. How else are you expected to solve the problems?

For the derivative, you may proceed as you did with separate TERMS, but not FACTORS. Do you know the Product Rule? I'm guessing this is another item missing from your background simply because no one ever told you you should know it. Really, there appears to be something wrong with your curriculum. Please have a chat with your teacher or materials provider and ask them to explain this deficiency.

Product Rule: If R(x) = g(x)*h(x), then R'(x) = g(x)*h'(x) + h(x)*g'(x)

In your case: g(x) = 2x and h(x) = 900 + 32x - x^2, giving R'(x) = 2x*(32-2x)+(900 + 32x - x^2)*2

As Elizabeth indicated, you can verify this by simple multiplication. R(x) = 2x(900+32x-x^2) = 1800x + 64x^2 - 2x^3

With a little algebra, you should see that the two expressions are the same.
 
tkhunny said:
I just don't understand the calculus requirements in a course where calculus is not a prerequisite.
Click to expand...
I think the poster's remarks were meant to say that the poster has completed a pre-calculus algebra course, and is now currently taking an elementary (differential) calculus course. I could be wrong, of course.... :oops:

Eliz.
 
finding the marginal revenue when x=14 you have to use the product formula beacuse there are 2 terms seperated by multiplication...


but I dont understand the last question, what kind of comparison is asked on this question....
 
gusyve said:
finding the marginal revenue when x=14 you have to use the product formula beacuse there are 2 terms seperated by multiplication...
f(x)
Click to expand...
Please check your definitions. Separation by multiplication creates "factors", not "terms". These words have specific meanings and their more generic usage is confusing.
 
Sorry about that , I ment to say factors and as it was explained before the right way to do it I think is using the Product Formula, the answer that I had was $3200, correct me if sam wrong , but am still having questions on the last question.....
 
Clear it up by producing the derivitive. What do you get for R'(x)?
 
Please work on your notation. On the left, you have R(14). On the right, you have R'(x) for x = 14.

Since this gives 2416, what was it that you said was 3200?

R(14) = 3226
R(15) = 3465
R(15) - R(14) = 3465 - 3226 = 2394

R'(x) = 1800 + 128x - 6x^2

R'(14) = 2416

Compare 2416 to 2394. This is the point of the exercise.
 
ok I have all the way to substracting R(15)-R(14) , but on the quenstion that indicates to find the marginal revenue when x=14
I got it but I think instead of 5x^2 is 6x^2
 
you fixed it, good, we are on the same page now, hopefully all this comments were helpfull to others as it was to me, and thanks to all the help provided to us, to those who replied our questions thank you.

GUSYVE
 
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