# Help with finding rate of increase using product/quotient rule

• May 5th 2009, 10:47 AM
elong
Help with finding rate of increase using product/quotient rule
I've been having trouble with a particular problem from my Calculus book in the Product and Quotient rules chapter.

I was hoping someone on this forum could help me out. Thanks in advance! (Happy)

Question:

Suppose the price of an object is $14 and 12,000 units are sold. The company wants to increase the quantity sold by 1200 units per year, while increasing the revenue by$20,000 per year. At what rate would the price have to be increased to reach these goals?
• May 5th 2009, 11:14 AM
Jameson
Quote:

Originally Posted by elong
I've been having trouble with a particular problem from my Calculus book in the Product and Quotient rules chapter.

I was hoping someone on this forum could help me out. Thanks in advance! (Happy)

Question:

Suppose the price of an object is $14 and 12,000 units are sold. The company wants to increase the quantity sold by 1200 units per year, while increasing the revenue by$20,000 per year. At what rate would the price have to be increased to reach these goals?

If x is the price of each object, than the price, P, times x is the revenue. So $R=Px$. For the first part, P=$14 and x=12,000 so $R=14 \times 12,000=168,000$. Now if the amount sold has to been increased by 1,200 units per year this means that the new total objects sold is 12,000+1,200=13,200. Follow? So now we know the units sold and the desired revenue, but not the price. Let's set up the equation again: $R=Px$ so $20,000=P(13,200)$. Now solve for P and solve for how much this new price has increased from the old. edit: Your problem might be a little different than this. I don't know if the first line means those products were sold once or that's the yearly amount. • May 5th 2009, 12:56 PM elong Thank you. I do follow what you are saying and it does seem logical, but what is throwing me off is the fact that I think we are suppose to either use the product or quotient rule to solve this problem. The following is a similar question that I solved correctly. Ques: Suppose the price of an object is$20 and 20,000 units are sold. If the price increases at a rate of $1.25 per year and the quantity sold increases at a rate of 2000 per year, at what rate will revenue increase? Answer: R' = Q'P + QP' (Product Rule) At a certain moment of time (call it t0) we are given P(t0) = 20. Q(t0) = 20,000 (items) P'(t0) = 1.25 Q'(t0) = 2,000 (items/year) --> R'(t0) = 2,000(20) + (20,000)1.25) = 65,000$ per year