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.
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)
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).
Ok this is what I got.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?
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
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
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
emosniper said:What do you mean by 'sign'? << Positive or negative
<< Positive. sorry for my ignorance.Subhotosh Khan said:What do you mean by 'sign'? << Positive or negative
emosniper said:<< Positive. sorry for my ignorance.
Why should it be positive ?
Q^3 is getting subtracted - isn't it??
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.
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
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?
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.
[/quote]mmm4444bot said:Since the answer is a dollar amount, I would prefer to see $16,318.44 as a final result.