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Unformatted text preview: EXAM 2 Section xxx October 7, 2005 NAME: Make sure to read the question carefully and answer the question that is asked. Show ALL relevant work so that partial credit may be given and indicate where the solution is. Lack of sufficient work may result in a loss of credit, even if a correct answer is given. Good luck!! “On my honor, as a University of Colorado at Boulder student, I have neither given nor received unautho rized assistance on this work.” YOUR SIGNATURE: 1. Marginal Functions The cost (in dollars) to produce x color printers is given by C ( x ) = 400 x + 100000 . The marketing department has also established that the demand for these printers is given by p = . 05 x + 700 , where p denotes the printer’s unit price (in dollars) and x denotes the quantity demanded. (a) (3 points) What is the revenue function R ( x )? Solution: The revenue can be found by multiplying price p by quantity x . So, R ( x ) = px = ( . 05 x + 700) x = . 05 x 2 + 700 x. (b) (7 points) Find the marginal profit function and verify that it is equal to zero when x = 3000. Solution: Profit is “revenue minus cost” and “marginal” indicates the derivative. P ( x ) = R ( x ) C ( x ) = ( . 05 x 2 + 700 x ) (400 x + 100000) = . 05 x 2 + 300 x 100000 Taking the derivative, we find the marginal profit function to be P ′ ( x ) = . 1 x + 300 ....
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 Spring '08
 JOHANSON
 Calculus, Derivative, function chain rule, 4x3

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