SOLUTION: Hi, I'll write the problem word for word in case you can't find it: Toy manufacturing: After being in business for t years, a toy manufacturer is making x = 5000 + 50t + 10

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Question 187397This question is from textbook Precalculus
: Hi,
I'll write the problem word for word in case you can't find it:

Toy manufacturing: After being in business for t years, a toy manufacturer
is making x = 5000 + 50t + 10t^2 GI Jimmy toys per year. The sale
price p in dollars per toy has risen according to the formula
p = 10 + 0.5t. Write a formula for the manufacturer's yearly revenue as
a. a function of time t.
b. a function of price p.

I've used the formula:
(R)Revenue = (P)Price per item * (x)Number of items sold,
and came up with: R(t)=(10+0.5t)*(5000+50t+10t^2) for part a. I'm not sure if this is right or not. Part b I'm not sure either. I had: R(p)=p(5000+50t+10t^2).
Any help at this point would be really appreciated.
Thank you,
Lynn Scott
 This question is from textbook Precalculus

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You are almost there. Part a is technically correct, although you should finish it by multiplying the price binomial across the quantity trinomial:



The problem with your answer to Part b is that what you are saying is a function of p is actually a function of p and t.

What you need to do is take the price function of t:



and solve it for t,

,

and then substitute this expression for t into your function for price, thus:



Simplifying to a single polynomial expression is left as an exercise for the student.

John