SOLUTION: The monthly revenue R achieved by selling x wristwatches is figured to be
R(x)=75x−0.2x^2. The monthly cost C of selling x wristwatches is C(x)=28x+1650.
(a) How many
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R(x)=75x−0.2x^2. The monthly cost C of selling x wristwatches is C(x)=28x+1650.
(a) How many
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Question 1138948: The monthly revenue R achieved by selling x wristwatches is figured to be
R(x)=75x−0.2x^2. The monthly cost C of selling x wristwatches is C(x)=28x+1650.
(a) How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue?
(b) Profit is given as P(x)=R(x)−C(x). What is the profit function?
(c) How many wristwatches must the firm sell to maximize profit? What is the maximum profit?
(d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue. Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! Revenue=75x-0.2x^2
this is a quadratic with maximum at vertex where x=-b/2a=-75/-0.4=187.5
maximum revenue is $7031.20 for both 187 and 188 watches.
profit is the difference between these two, or -0.2x^2+47x-1650
This is maximized for x=-47/-0.4 or 117.5 watches
f(117.5)=$1111.25
they differ because there are two different quadratics, basically. The third graph has a difference between the two. Cost increases linearly, revenue will increase up to a point where beyond which more being sold and then decrease, either because of decrease in demand, oversupply, or other factors.
