The revenue from selling q items is

Question

R(q) = 600q − q^2,
and the total cost is
C(q) = 150 + 50q.
Write a function that gives the total profit earned.

It is my understanding that profit = revenue - costs.
So when I tried to write the function for total profit earned, I subtracted the two.
(600q-q^2) - (150 + 50q) and got 600q-q^2-150-50q so -q^2-550q-150

Is this answer wrong? I don't know how to get the right answer.

Answer 1

The second part of this questions asks:
Find the quantity which maximizes the profit

Please help me solve this part as well.

I know that profit is maximized when the derivative of revenue equals the derivative of cost.. but how do I get there?

Answer 2

well, just find the two derivatives:

dR/dq = 600-2q
dC/dq = 50

so, you want

600-2q = 50
q = 275

Note that this is the value of q at the vertex of the parabola, q = -b/2a = -550/-2. Note the typo in your final function. Should be +550q, not -550q

Answer 3

Thank you so much!