Econonics: R=1200Q-2Q2, C=Q3-61.25Q2+1528.5Q+2000, get R & C

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emosniper

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Nov 17, 2008
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This is a Cubic equation but I dont know how to get a real answer from these.
R = Revenue
C = Cost
Q = Quantity

R(Q) = 1200Q – 2Q2
C(Q) = Q3 – 61.25Q2 + 1528.5Q + 2000

How do you solve these?
I need to get R and C.
 
Re: Econonic Math Problem

emosniper said:
This is a Cubic equation but I dont know how to get a real answer from these.
R = Revenue
C = Cost
Q = Quantity

R(Q) = 1200Q – 2Q2
C(Q) = Q3 – 61.25Q2 + 1528.5Q + 2000

How do you solve these?
I need to get R and C.
Click to expand...

As such your question does not make sense to me. You need to get R & C - under what condition? Maximum? Minimum? For given Q?

Please share with us your work, indicating exactly where you are stuck, so that we know where to begin to help you.
 
Re: Econonic Math Problem

Let Revenue and Cost be functions of the Quantity of a good sold and produced in a given period of time.

R(Q) = 1200Q – 2Q2
C(Q) = Q3 – 61.25Q2 + 1528.5Q + 2000

a. What is the Profit function?
b. What are the possible profit maximizing outputs of Q?
c. What is the profit maximizing output of Q?
d. How much profit is made per period?


Thats all I got. I don't know how you can complete such a math problem........ Copied from website...
 
Re: Econonic Math Problem

emosniper said:
Let Revenue and Cost be functions of the Quantity of a good sold and produced in a given period of time.

R(Q) = 1200Q – 2Q2
C(Q) = Q3 – 61.25Q2 + 1528.5Q + 2000

a. What is the Profit function? <<<<<< What is the definition of profit function - given cost and revenue?
b. What are the possible profit maximizing outputs of Q? <<< How do you find maximum/minimum of a function?(Hint: derivative)
c. What is the profit maximizing output of Q?<<< How do you find maximum/minimum of a function?(Hint: derivative)

d. How much profit is made per period? <<<< Combine answers from (a) and (c)
Click to expand...
 
Re: Econonic Math Problem

I believe the Profit Function is R(Q) - C(Q).
I just don't see how you find one real number. I need to figure out this first, how to solve for R(Q) and C(Q).
 
Re: Econonic Math Problem

emosniper said:
I believe the Profit Function is R(Q) - C(Q).
I just don't see how you find one real number. I need to figure out this first, how to solve for R(Q) and C(Q).
Click to expand...

<<< How do you find maximum/minimum of a function?(Hint: derivative)

Do you know how to calculate the derivative of a function?
 
Re: Econonic Math Problem

like b^2 4ac?

emosniper said:
R(Q) = 1200Q – 2Q2
C(Q) = Q3 – 61.25Q2 + 1528.5Q + 2000

a. What is the Profit function?
b. What are the possible profit maximizing outputs of Q?
c. What is the profit maximizing output of Q?
d. How much profit is made per period?
Click to expand...
Ok this is what I got.
A. Q^3 + 59.25Q^2 - 328.5Q - 2000
B. Q = 3, 36.5
C. Q = 36.5
For D I think I have to plug in C to P(Q).
D. 113572.6875

Could someone check my work?
Thanks Subhotosh Khan, for the (Hint: derivative)
 
Re: Econonic Math Problem

emosniper said:
Ok this is what I got.
A. Q^3 + 59.25Q^2 - 328.5Q - 2000 <<< Incorrect - show detailed work for correction
B. Q = 3, 36.5
C. Q = 36.5 For D I think I have to plug in C to P(Q).<<< Correct
D. 113572.6875<<< Incorrect - show detailed work for correction
Click to expand...
 
So did I get B & C right?

With A I just did:
(1200Q – 2Q2) - (Q3 – 61.25Q2 + 1528.5Q + 2000), which equals R(Q) - C(Q).

And with D. I plugged in. 36.5 = Q, for {P(Q) = Q^3 + 59.25Q^2 - 328.5Q - 2000}.

Letter A is right. I believe, because it is asking for the function, and to find the function you do R(Q) - C(Q).
 
emosniper said:
So did I get B & C right?

With A I just did:
(1200Q – 2Q2) - (Q3 – 61.25Q2 + 1528.5Q + 2000), which equals R(Q) - C(Q). <<< What is the sign of Q^3 in this expression
Click to expand...
 
Subhotosh Khan said:
(1200Q – 2Q2) - (Q3 – 61.25Q2 + 1528.5Q + 2000), which equals R(Q) - C(Q). <<< What is the sign of Q^3 in this expression
Click to expand...

What do you mean by 'sign'?
 
Subhotosh Khan said:
What do you mean by 'sign'? << Positive or negative << Positive. sorry for my ignorance.

Why should it be positive ? << Ok I see that mistake Q^3 should be negative.
Click to expand...
 
So my new answers.

A. P(Q) = -Q^3 + 59.25Q^2 - 328.5Q - 2000

Then for B & C you use the derivative.
Which would look like this:
P(Q) = -3Q^2 + 118.5Q -328.5
Then from there I could use the Quadratic Formula?
Right?
 
emosniper said:
So my new answers.

A. P(Q) = -Q^3 + 59.25Q^2 - 328.5Q - 2000

Then for B & C you use the derivative.
Which would look like this:
P(Q) = -3Q^2 + 118.5Q -328.5
Then from there I could use the Quadratic Formula?
Right?<<< Correct
Click to expand...
 
emosniper said:
So my new answers.

A. P(Q) = -Q^3 + 59.25Q^2 - 328.5Q - 2000

Then for B & C you use the derivative.
Which would look like this:
P(Q) = -3Q^2 + 118.5Q -328.5
Then from there I could use the Quadratic Formula?
Right?
Click to expand...

Ok now:
-118.5 (+-) [sqrt]118^2-4(-3)(328.5)[/sqrt]
*/skipped some*/
(-118.5 (+-) 100.5) / -6?

Answer For B:
Q = 3, 36.5

Right?

Answer For C:
36.5

Answer For D:
Q=36.5 in {P(Q) = -Q^3 + 59.25Q^2 - 328.5Q - 2000}.
Which makes: 16318.4375.

Right?
 
emosniper said:
... Answer For B:

Q = 3 or Q = 36.5

Right? Yes, these are the two roots, but is a fractional quantity Q okay in this exercise?

Answer For C:

36.5 It is definitely not 3 because P(3) is negative.

Answer For D:

Q = 36.5 in {P(Q) = -Q^3 + 59.25Q^2 - 328.5Q - 2000}.

Which makes: 16318.4375. Yes, but these two lines are much clearer (and easier!) as simply:

P(36.5) = 16318.4375

Ease and clarity are exactly why function notation was developed.

Right? Since the answer is a dollar amount, I would prefer to see $16,318.44 as a final result.
Click to expand...
 
Re:

mmm4444bot said:
Since the answer is a dollar amount, I would prefer to see $16,318.44 as a final result.

Click to expand...
[/quote]

How do you know this is not a Chinese Currency problem? :twisted:
 
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