anonymous
  • anonymous
Help with problem - WILL REWARD! The estimated monthly profit realizable by Hanover Jones Inc, for manufacturing and selling x units of its toy boats is P(x) = -4x^2+988x - 250 dollars. a. Determine how many toy boats should the Hanover Jones Inc. produce per month in order to maximize its profits. b. What is the maximum monthly profit realizable?
Mathematics
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SOLVED
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chestercat
  • chestercat
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AbdullahM
  • AbdullahM
Do you know how to find the vertex of an equation?
anonymous
  • anonymous
I am struggling with that
TheCatMan
  • TheCatMan
Try solving as y=-4x^2+988X-250 by by putting it in standard form because my teacher showed a variable such as P(x) is the same as a y

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TheCatMan
  • TheCatMan
y=16x+988x-250 -16x y-16x=988x-250 /x /x y-16= 988-250 +16 +16 y= 754 use as much of this as possible
TheCatMan
  • TheCatMan
y is P(x)
AbdullahM
  • AbdullahM
You can not do that. That isn't even possible to do...
AbdullahM
  • AbdullahM
The x-coordinate of the vertex for the equation: \(\sf \color{blue}{a}x^2+\color{red}{b}x+c\) is \(\sf\Large h=\frac{-\color{red}{b}}{2\color{blue}{a}}\) The h is because the vertex is written as \(\sf (h,k)\) so the x-coordinate of the vertex would be 'h'.
AbdullahM
  • AbdullahM
@TheCatMan What you are suggesting to do is: \(\sf\LARGE \frac{y-16x}{x}=\frac{988x-250}{x}\) and you have to use this rule when simplifying: \(\sf\Large \frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\)
TheCatMan
  • TheCatMan
well im not the best at math i will admit so i cant say much
TheCatMan
  • TheCatMan
i really should be demoted for lack of brain power.
AbdullahM
  • AbdullahM
@ahl829 Can you calculate the 'h' value from what I have given you? That will give you your answer for part a.
TheCatMan
  • TheCatMan
the equation that you wrote is like russian to me since im only beginning Algebra 1
anonymous
  • anonymous
I believe so. Using your equation - i calculated: h=-b/2a = -988/2(-4) = -988/-8 = 123.50 The $123.50 should transfer to the answer for question a of how many boats per year to be profitable. Since you can't make 1/2 a boat - it would be rounded to 124. Then I would take 124 and plug it into the original equation such as: P(x) = -4(124)^2+988(124) - 250 = $60,758 -- which would answer part b of maximum monthly profit ? Thats how I thought it through in my head - is that correct?

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