the Profit formula for a given toy is P= -20s2+1400s-12,000 P 20 s 2 1400 s 12 000 , what selling price should they set to maximize profit?

Question

I need help with this word problem I don't understand it.

Answer 1

If the formula is a quadratic, then you need to find the vertex using the formula

 

h = -b/(2a)   ------> x-coordinate of vertex

 

 

Then you will evaluate P when s=h.

Answer 2

Hi Ayillia,

 

The equation is a parabola. If you graph it, the peak of the parabola is the S you need to maximize P. 

 

Hope this helps

Answer 3

It looks like your profit equation is:

 

P = -20s² + 1400s - 12000

 

This graphs as a parabola opening downward where profit is a function of selling price.

The maximum profit will be P value at the vertex of the parabola.

 

For a quadratic of format y= ax² + bx + c the x value of the vertex is

at the value x=-b/2a.  Your equation is a quadratic, just calling the variables

P and s instead of y and x

 

a = -20, b=1400, c = -12000

 

-b/2a = -1400/[2(-20)]=-1400/-40 = 35

 

Your "s" value at the vertex is $35 for selling price.

 

Note:  If you want to determine the profit at that point,

plug in 35 for s in the equation and solve for P