plzz help.. i dont know if i did it right or not:
macro manufacturing company estimates that its profit P, in thousands of dollars, after producing x thousand units can be modeled by the equation P=-4x^2+24x-1
will the profit ever be $12000?
when i did it, i made $1200 equal to p.
12000=-4x^2+24x-1 and the answer i got was that it will reach 12000 dollars after 2994 units. but im not sure if its right.... HELP!!!
THNXX :)
macro manufacturing company estimates that its profit P, in thousands of dollars, after producing x thousand units can be modeled by the equation P=-4x^2+24x-1
will the profit ever be $12000?
when i did it, i made $1200 equal to p.
12000=-4x^2+24x-1 and the answer i got was that it will reach 12000 dollars after 2994 units. but im not sure if its right.... HELP!!!
THNXX :)
-
You don't actually have to solve that ugly equation!
Just find the vertex; since the leading coefficient is negative there will be a maximum value.
-B/(2A) = -24/-8 = 3
The function is at its maximum when x = 3
The maximum value of P is then -4(3)^2 + 24(3) - 1, or 35. In thousands, the maximum profit is then $35000. So the answer is yes.
If you want to find WHEN it reaches $12000, then set it equal to 12 rather than 12000, since the profit is in thousands.
12 = -4x^2 + 24x - 1
0 = -4x^2 + 24x - 13
This is unfactorable, so using the quadratic formula, x = (-24 ± √(576 - 208))/-8 which simplifies to
(-24 ± 4√23)/8 or approximately 0.6 and 5.4.
Just find the vertex; since the leading coefficient is negative there will be a maximum value.
-B/(2A) = -24/-8 = 3
The function is at its maximum when x = 3
The maximum value of P is then -4(3)^2 + 24(3) - 1, or 35. In thousands, the maximum profit is then $35000. So the answer is yes.
If you want to find WHEN it reaches $12000, then set it equal to 12 rather than 12000, since the profit is in thousands.
12 = -4x^2 + 24x - 1
0 = -4x^2 + 24x - 13
This is unfactorable, so using the quadratic formula, x = (-24 ± √(576 - 208))/-8 which simplifies to
(-24 ± 4√23)/8 or approximately 0.6 and 5.4.