how to solve: find max profit from f(x) = -1.2x^+180x-280

georgebaseball

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hello, could you please explain me this problem

Profit: The Holley Bert company earns a weekly profit according to the function f(x) = -1.2x^+180x-280 where x is the number of rocking chairs built and sold.

a) Find the number of rocking chairs that the company must sell in a week to obtain the maximum profit.
b) Find the maximum profit.

I really appreciate your help. I've been trying to solve those kind of exercises, but I just can't do it.
 
Re: how to solve this problem, please

georgebaseball said:
hello, could you please explain me this problem

Profit: The Holley Bert company earns a weekly profit according to the function
f(x) = -1.2x^+180x-280 where x is the number of rocking chairs built and sold
a) find the number of rocking chairs that the company must sell in a week to obtain the maximum profit.
b, find the maximum profit


I really appreciate you help, I've been trying to solve those kind of exercises, but i just can't do it.

What you've got is a function in this form:

f(x) = ax<SUP>2</SUP> + bx + c

I hope that you recognize that this type of function is a parabola. I also hope that you recognize that if "a" in this equation is negative (as it is in your example), the parabola opens downward and that the function has a maximum value at the vertex of the parabola.
1
The x-coordinate of the vertex of a parabola with equation f(x) = ax<SUP>2</SUP> + bx + c occurs when x = -b/2a

Ok...in your equation, a = -1.2 and b = 180

So, -b / 2a = (-180) / 2*(-1.2)

Do the arithmetic....the result will be the x-coordinate of the vertex of the parabola. Use this number as x in f(x)....and find the resulting value which is the maximum value of the function.
 
Re: how to solve: find max profit from f(x) = -1.2x^+180x-28

Mrspi , I really appreciate you help/

Thank you so much.
 
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