Question 187397
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You are almost there.  Part a is technically correct, although you should finish it by multiplying the price binomial across the quantity trinomial:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ R(t)=(10+0.5t)(5000+50t+10t^2) = 50000 + 3000t + 25t^2 + 5t^3]


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


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


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  P(t) = p = 10 + 0.5t]


and solve it for <i>t</i>,


*[tex \LARGE \ \ \ \ \ \ \ \ \ \   t = 2p - 20],


and then substitute this expression for <i>t</i> into your function for price, thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  R(p)=p(5000+50(2p-20)+10(2p-20)^2)]


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


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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