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>
1/10=x hope that helps a bunch
Answer:
k = (6/15)
Step-by-step explanation:
The equation is:
6*(x + 1) + 2 = 3*(k*5*x + 1) + 3
To have no solutions, we need to have something like:
x + 7 = x + 4
where we can remove x in both sides and end with
7 = 4
So this equation is false, meaning that there is no value of x such that this equation is true, then the equation has no solutions.
First, let's try to simplify our equation:
6*(x + 1) + 2 = 3*(k*5*x + 1) + 3
6*x + 6 + 2 = 3*k*5*x + 3*1 + 3
6*x + 8 = 15*k*x + 6
if 15*k = 6, then the system clerly has no solution.
then:
k = 6/15
then we get:
6*x + 8 = (6/15)*15*x + 6
6*x + 8 = 6*x + 6
8 = 6
The system has no solutions.
Answer:
7
Step-by-step explanation:
Formula=area of base x height / 3
A= ( 3 x 1 ) x 7 / 3
A= 3 x 7 / 3
A= 21 / 3
A= 7
Answer: 24.6 inches
Step-by-step explanation: Since it's a rectangle, and not a rectangular prism, that means it's 2D. Length is the long sides on the top and bottom, and width is the shorter sides on it's left and right. So since there's two of each, just do 8.1 + 8.1 + 4.2 + 4.2 and you have your answer!
