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:
20%=8
10%=?
by cross multiplications,
10×8=80
80÷20=4
Hence the answer is 4.
Answer:
X=6
Step-by-step explanation:
Move the variable to get 9x-7x=12
collect like terms to get 2x=12
divide to get 6
Answer: Hermès is incorrect. The opposite of 9 is -9.
Explanation: In this question, Hermès gives an incorrect answer, claiming that the opposite of 9 is also 9. To find the correct answer, let’s first look at his reasoning. He was right in one thing- to find the opposite of a number, we need to find one that shares the same distance from zero. However, he was wrong in believing that the number had to be exactly the same. To find the opposite number, find the same distance from zero in the opposite direction. In this case, the distance from zero is 9. Go in the opposite direction from zero, 9 times. This would give you an answer of -9. Because of this, the opposite of 9 is -9.
Hope this helps! Comment below for more questions.
Answer:Any number
Step-by-step explanation:
