Answer:
Step-by-step explanation:
(x) = (1100 + x) (100 - .05(x-1100))
This is a quadratic, graphs as a parabola that opens downward. A maximum cam be found.
The zeros of the function are
(1100 + x) = 0 ..... or ..... [100 - .05(x-1100)] = 0
x = -1100 is the left x-intercept.
[100 - .05(x-1100)] = 0
100 = .05(x-1100)
2000 = x - 1100
x = 3100 is the right intercept.
Maximization of profits is at the mid point of the zeros (x-intercepts)
(3100 + -1100)/2 = 1000
1100 + 1000 = 2100 trees should be planted to maximize profits.
f(x) = (1100 + 1000) (100 - .05(1000-1100))
f(x) = (2000) (105) = 220,500 is the maximum profit.
I hope this helps!
It should open up because the a which is 4 is positive
Here is our profit as a function of # of posters
p(x) =-10x² + 200x - 250
Here is our price per poster, as a function of the # of posters:
pr(x) = 20 - x
Since we want to find the optimum price and # of posters, let's plug our price function into our profit function, to find the optimum x, and then use that to find the optimum price:
p(x) = -10 (20-x)² + 200 (20 - x) - 250
p(x) = -10 (400 -40x + x²) + 4000 - 200x - 250
Take a look at our profit function. It is a normal trinomial square, with a negative sign on the squared term. This means the curve is a downward facing parabola, so our profit maximum will be the top of the curve.
By taking the derivative, we can find where p'(x) = 0 (where the slope of p(x) equals 0), to see where the top of profit function is.
p(x) = -4000 +400x -10x² + 4000 -200x -250
p'(x) = 400 - 20x -200
0 = 200 - 20x
20x = 200
x = 10
p'(x) = 0 at x=10. This is the peak of our profit function. To find the price per poster, plug x=10 into our price function:
price = 20 - x
price = 10
Now plug x=10 into our original profit function in order to find our maximum profit:
<span>p(x)= -10x^2 +200x -250
p(x) = -10 (10)</span>² +200 (10) - 250
<span>p(x) = -1000 + 2000 - 250
p(x) = 750
Correct answer is C)</span>
To write this as an improper fraction you would multiply 9 by 1 then add your product to the numerator.
9x1=9
9+8=17
17/9
Hoped this helped!
