Quiz04_Solutions - QUIZ 4 SOLUTIONS#1 We want a linear...

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QUIZ 4 SOLUTIONS #1: We want a linear function relating price to number of tickets sold. We are told that an increase of $5 results in a decrease of 3,500 tickets. Our x is price, our f(x) is tickets, so the slope of our function is (change in # tickets / change in price) = -3500/$5 = -700. The y-intercept can be found if we let x=$15, y=24,500, and m=-700, so: b mx y + = Æ b + = ) 15 ( 700 500 , 24 Æ b=35,500. So #1a is 000 , 35 700 ) ( + = x x s Revenue = price * # tickets sold, so x x x x s x r 35000 700 * ) ( ) ( 2 + = = (#1b)
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Unformatted text preview: This is what you want to maximize, so let a=-700, b=35000, so 25 $ 1400 35000 2 = − − = − a b So the optimal ticket price is x=$25. (#1c) Using your model from part a, set s(x)=0 Æ 50 $ ) ( 700 35000 = = − x x As you can see, at x=25, the function has maximum value. Theoretically at x=50, no one would attend, and at x=0 you could sell 35,000 tickets but since price=0, revenue=0 #2:...
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  • Fall '08
  • WEY
  • Calculus, Linear function, Tickets, Optimal ticket price

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