Answer:-12 and -25
Step-by-step explanation:
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:
k = 4
Step-by-step explanation:
-9 +8k = 7+4k
Subtract 4k from each side
-9 + 4k = 7
Add 9 to each side
4k = 16
Divide by 4
k = 4
Plug in the value you got for k:
-9 + 8(4) ? 7 + 4(4)
-9 + 32 ? 7 + 16
23 ? 23
23 = 23
5/10 kilogram per 1/6 minutes = 5/10 * 6 = 30/10 = 3 kilograms/min
3 kilograms/min * 60 min/hour = 180 kilograms/hour
180 kilograms/hour * 24 hours/day = 4320 kilograms/day
4320 kilograms/day * 365.25 days/year = 1,577,880 kilograms/year
