math

The revenue from selling q items is
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.

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  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?

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  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

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  3. Thank you so much!

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