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>
Arc length = 2 π R (C/360)
where:
C is the central angle of the arc
R is the radius of the arc
arc length = 2 π R (137/360) = 2.39R
<h2>
The area of the framed photograph = 1156 
</h2>
Step-by-step explanation:
Given,
The length of photograph (l) = 14 inches and
The breadth of photograph (b) = 10 inches
To find, the area of the framed photograph = ?
We know that,
The area of the framed photograph = (l + 2b)(l + 2b)
= (14 + 2 × 10) (14 + 2 × 10)
= (14 + 20) (14 + 20)
= (34) (34)
= 1156
∴ The area of the framed photograph = 1156
Answer:
answer b
Step-by-step explanation:
hope that helps
Answer:
192 inches because 16×12=192
