## anonymous one year ago 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?

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1. AbdullahM

Do you know how to find the vertex of an equation?

2. anonymous

I am struggling with that

3. 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

4. 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

5. TheCatMan

y is P(x)

6. AbdullahM

You can not do that. That isn't even possible to do...

7. 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'.

8. 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: $$\sf\Large \frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$$

9. TheCatMan

well im not the best at math i will admit so i cant say much

10. TheCatMan

i really should be demoted for lack of brain power.

11. AbdullahM

@ahl829 Can you calculate the 'h' value from what I have given you? That will give you your answer for part a.

12. TheCatMan

the equation that you wrote is like russian to me since im only beginning Algebra 1

13. 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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