Question 173539This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: 18) The We Make Widgets Company manufactures widgets. They find that when they charge d dollars for each widget, their income, I(d) can be expressed by the formular I(d) = -120d^2 + 14,400d + 100. What price should they charge to maximize their income? If this price is charged, what is their maxium income?
Please can someone help me and show work, step by step?
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This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
Found 2 solutions by nerdybill, josmiceli:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 18) The We Make Widgets Company manufactures widgets. They find that when they charge d dollars for each widget, their income, I(d) can be expressed by the formular I(d) = -120d^2 + 14,400d + 100. What price should they charge to maximize their income? If this price is chargeThe d coordinate = -14400/2(-120)
d, what is their maxium income?
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Looking at the 'a' coefficient of the given equation:
I(d) = -120d^2 + 14400d + 100
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We see that it is negative -- meaning that it is a parabola that is opened downward. So, if we simply find the "vertex" of the equation, we'll find the "maximum".
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For additional info on vertex form of a parabola:
http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php
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The vertex is located at:
The d coordinate = -b/2a
The d coordinate = -14400/2(-120)
The d coordinate = -14400/(-240)
The d coordinate = 60
What price should they charge to maximize their income? $60
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what is their maxium income?
Plug it back into the original formula:
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I(d) = -120d^2 + 14,400d + 100
I(60) = -120(60)^2 + 14,400(60) + 100
I(60) = -120(3600) + 14400(60) + 100
I(60) = -432000 + 864000 + 100
I(60) = 432000 + 100
I(60) = $432,100
Answer by josmiceli(19441)  (Show Source):
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