MATH HELP. algebra 2....?

Question

(my brother's hw)


The profit P (in hundreds of dollars) that a company makes depends on the amount x (in hundreds of dollars) the company spends on advertising according to the model:
P = 230 + 20x - .5x²
What expenditure for advertising will yield a maximum profit?

Answer 1

you don't need to plot the curve.

since p= -0.5x^2 + 20x + 230 has a negative coeff a (-0.5)
the curve opens downwards, so there is a max.

the vertex is at x= -b/2a = -20/(-2x0.5) = 20
same answer as the answers above using calculus.

Answer 2

Using only algebra you will have to plot the curve to see where the maximum point is

Using calculus, get the first derivative

P' = 20 - x

Set to zero

20 - x = 0

20 = x

$2000 advertising yields a maximum profit

Answer 3

Max profit will come when P' = 0

P' = 20 - x
So 0 = 20 - x
x = 20

When 2,000 dollars is spent on advertising, profit will be maximized.

Answer 4

http://www.mathalino.com

This problem can easily be done in Differential Calculus but if you want to answer it in Algebra just plot the curve with P as the y-axis. Your graph will be a parabola, find its vertex and take the y-coordinate of that vertex, that is the maximum profit.

Answer is 20,000

http://www.mathalino.com