The revenue (in dollars) for selling q items is given by r ( q ) = 348 q − 2 q 2 and the costs (in dollars) of producing q items is given by c ( q ) = 100 + 60 q . find the quantity that gives the maximum profit.

The quantity of 72 that gives the maximum profit of 10268

Explanation:

The profit function p(q) is given by the difference between the revenue and the cost function,

                   P(q) = R(q) - C(q)

The revenue (in dollars) for selling q items is given by  

The costs (in dollars) of producing q items is given by C(q)= 100 + 60q

The above profit function is a downward opening parabola. Its maximum value occurs,

Maximum value,

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