Total profit P is the difference between total revenue R and total cost C. Given the following​ total-revenue and​ total-cost functions, find the total​ profit, the maximum value of the total​ profit, and the value of x at which it occurs. R(x)=1300x-x^2
C(x)=3300+20x

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The profit function is:

The maximum value is 406, 300 occurring when x = 640.

Step-by-step explanation:

The revenue function is:

And the cost function is:

Then the total profit function will be:

This is a quadratic function.

Therefore, the maximum value of the total profit will occur at its vertex point.

The vertex of a quadratic is given by:

In this case, a = -1, b = 1280, and c = -3300.

Then the point at which the maximum profit occurs is at:

And the maximum profit will be: