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>
In 10 months Lisa will have paid the same amount as Kelly, but in month 11 she will have paid more.
Answer:
$1.25 per game
Step-by-step explanation:
Answer:
Step-by-step explanation:
The correct question is
Susan works as a tutor for $10 and hour, and as a waitress for $11 an hour. This month, she worked a combined total of 90 hours at her two jobs. Let t be the number of hours Susan worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month
Let
t -----> the number of hours that Susan work as a tutor
y ----> the number of hours that Susan work as a waitress
z ---> the combined total dollar amount she earned this month
we know that
-----> equation A
we know that
The combined total dollar amount she earned this month is equal to the number of hours that Susan work as a tutor multiplied by $10 plus the number of hours that Susan work as a waitress multiplied by $11
----> equation B
substitute equation A in equation B
therefore
The expression for the combined total dollar amount is $(990-t)
