Math CentralQuandaries & Queries


Question from Megan, a student:

The weekly revenue for a company is R= -3p+60p+1060, were p is the price of the company's product. Find the maximum revenue for this company.

Megan, are you sure you don't have a typo in your question? I presume
you meant to write this:

R = -3p2 + 60p + 1060

This is a parabola opening downward. The vertical axis of the parabola is R (revenue) and the horizontal axis is p (price). Therefore if you want to know the maximum revenue (and the associated price to get that maximum revenue), you are asking to find the vertex of the parabola.

The vertex of a parabola is the point (h, k) when you transform the equation into the standard parabolic form:

R = a (p - h)2 + k

So transform your equation into this format (you will probably have to "complete the square" to do this) and you can just read off the value of k, which is the maximum revenue.

Hope this helps,
Stephen La Rocque.

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