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Study Guides > Finite Math

Putting It Together

You should recognize profit as a quadratic equation:

P = R − C = −20 + 12q − 0.5q2

We know that the maximum occurs at the vertex. The axis of symmetry is a vertical line that passes through the vertex. The equation for this line is [latex]\displaystyle q={-}\frac{{b}}{{2a}}={-}\frac{{12}}{{2(-0.5)}}={12}[/latex] . Thus our price should be set at $12. This will give us a profit of $108. That may not sound like a lot, but if profit, revenue and cost were measured in thousands of dollars, or even millions of dollars, then this is significant.

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