Calc
posted by Ben .
Demand is q=p^2+33p+9 copies of a book sold per week when price is p dollars. Can you help determine what price the company should charge to get the largest revenue?
I solved this as a Max Revenue problem and got x=0 and x=22 so the books should be sold for $22 each. IS THIS RIGHT?
Also, cost is C=9q+100 dollars to sell q copies of a book in a week. What price should the company charge to get the largest weekly profit? What is the max possible profit weekly profit and how can you be certain that the profit is maximized?
I got the profit function to be P=p(p^2+33p+9)9(p^2+33p+9)+100. I simplified this to P=(p^2+33+9)(p9+100). I then took the derivative using the product rule to get P'=2p+33(p9+100)+(1)(p^2+33p+9). I know I then need to set this equal to zero if it is right, I then have to factor and say which value maximizes profit. IS THIS RIGHT? Please help me to solve this part, I do not know how to solve P' equal to zero and factor

largest revenue is q*p
revenue=qp
dR/dq=d/dq (p^3 + 33p^2 + 9p)=0
solve that equation.
I get (22+22.3)/2= 22
Now, cost.
Profit= revenuecost
Profit= qp 9q+100
dP/dp= p(dq/dP) + q 9 dq/dp
where dq/dP=(2p+33) and q=p^2+33p+9
setting to zero
0=2p^2+33pp^2+33p+99(2p+33)
0=3p^2+48p33*9
check that, then use the quadratic equation to solve it. 
I see I made at least one error, in the constant. Check it line by line.

For the first part I took R' and set this equal to zero to get 22, is this right too.

I am confused on how you did the cost part. I think I got P' but I don't see this in your work. I know I have to set P' equal to zero but I don't know if I have to factor or something first

Yes, p=22 for max R.
On the second, profit, just start with revenuecost, both as a function of p, simplify it as as abest you can, then dProfit/dp=0 and solve for p. The factoring will take care of itself...you need to end up with a quadratic in standard form. 
I did simplify P' to be P'=2p+33(p9+100)+1(p^2+33p+9) now I have to set the derivative,P', equal to zero and I do not know how to solve it.

We did what Matt said but we do not know what to do next, our teacher told us to set the derivative equal to zero and then factor to get more than one answer and say which one maximizes the profit but we cannot solve P'=0

P'=2p+33(p9+100)+1(p^2+33p+9)=0
I didn't check that to make certain the derivative is correct. But if it is, gather terms, and
p^2+ (2+33+33)p + 3300 +9=0
check that.
Now use the quadratic equation to find the values of p that solve it.
Respond to this Question
Similar Questions

college algebra
Demand Equation: The price p, in dollars, and the quantity x sold of a certain product obey the demand equation x = 5p + 100, 0 (less than or equal to) p (less than or equal to) 20 a.) Express the revenue R as a funtion of x. b.) … 
Calc w/ Business
I have to determine the price that needs to be charged to obtain the largest revenue. q=p^2+33p+9 so R=p(p^2+33p+9) or =p^3+33p^2+9p I then need to take the derivative R'=3p^2+66p+9 Now I somehow need to solve for p to determine … 
math
A new software company wants to start selling DVDs with their product. The manager notices that when the price for a DVD is 20 dollars, the company sells 139 units per week. When the price is 34 dollars, the number of DVDs sold decreases … 
math
A new software company wants to start selling DVDs with their product. The manager notices that when the price for a DVD is 20 dollars, the company sells 139 units per week. When the price is 34 dollars, the number of DVDs sold decreases … 
math
A new software company wants to start selling DVDs with their product. The manager notices that when the price for a DVD is 20 dollars, the company sells 139 units per week. When the price is 34 dollars, the number of DVDs sold decreases … 
calculus
(1 pt) A new software company wants to start selling DVDs with their product. The manager notices that when the price for a DVD is 15 dollars, the company sells 132 units per week. When the price is 27 dollars, the number of DVDs sold … 
calculus
(1 pt) A new software company wants to start selling DVDs with their product. The manager notices that when the price for a DVD is 15 dollars, the company sells 132 units per week. When the price is 27 dollars, the number of DVDs sold … 
Math
Please show me how to set it up and to solve: A cell phone company sells about 500 phones each week when it charges $75 per phone. It sells about 20 more phones per week for each $1 decrease in price. The company's revenue is the product … 
calc
I have everything right but the last question asking how many cases per week The consumer demand equation for tissues is given by q = (97 − p)2, where p is the price per case of tissues and q is the demand in weekly sales. (a) … 
Calculus
ohaganbooks is offering a wide range of online books, including current bestsellers. a colleague has determined that the demand for the latest best selling book is given by q=(p^2)+33p+9 (18<p<28) copies sold per week when …