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>
Answer:
3*5^2
Step-by-step explanation:
75 is divisible by 3
75/3 = 25
25 is not divisible by 3, but it is divisible by 5.
25 = 5^2.
25/25 = 1. We are done.
D 2520 -------------------------------------------
13.1 an hour, 34 hours a week
13.1 x 34 = 445.4 a week
to find out how many weeks, divide 4300 and 445.4 which is 9.65 weeks, which is technically 10 weeks
it would take 10 weeks to earn 4300
Answer:
Step-by-step explanation:
se the graph to determine the input values that
correspond with f(x) = 1.
O x=4
O x= 1 and x = 4
O x= -7 and x = 4
O x= -7 and x = 2
6.
(-6, 4)
4
(1,4)
w
2
(-7, 1)
(2, 1) x
2
4
-8/ -6 -4 -2
-2
-4
