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:
3x-8=y
Step-by-step explanation:
Answer:
The median of this set is 45.
Step-by-step explanation:
To find the average velocity in a velocity-time graph at a particular interval, simply determine the gradient at that particular interval.
<span>a. average velocity= 4/1 </span>
<span>= 4m/s </span>
<span>b. average velocity from 1 to 2.5s= 6/(2.5-1) </span>
<span>= 4m/s </span>
<span>average velocity from 2.5 to 4.0s= 0m/s </span>
<span>average velocity from 0 to 4.0s= (4+0)/4 </span>
<span>= 1m/s </span>
<span>c. average velocity from 1.0 to 4.0s= (4/3)m/s </span>
<span>average velocity from 4.0 to 5.0s= 2/1 </span>
<span>= 2.0m/s </span>
<span>average velocity from 1.0 to 5.0s= ((4/3)+2)/4 </span>
<span>= (5/6)m/s </span>
<span>d. average velocity from 0 to 4.0s= 1.0m/s </span>
<span>average velocity from 4.0 to 5.0s= 2.0m/s </span>
<span>average velocity from 0 to 5.0s= (1.0+2.0)/5 </span>
<span>= (3/5)m/s </span>
0.007 divided by 0.001 = 7.0
Put as the brainliest answer if you think I helped you! Thank you so much!
