Marginal profit, and maximizing profit & average profit - Derivative Applications

Marginal profit, and maximizing profit & average profit

Lessons

Notes:

Marginal Profit (MP) is the additional profit that is gained when you increase the unit by one. It is also the derivative of the profit function. In other words,

MP=P(q)=R(q)C(q)MP = P'(q) = R'(q) - C'(q)

Average Profit (AP) is the amount of profit generated per unit. In other words,

AP(q)=P(q)q=R(q)C(q)qA P(q) = \frac{P(q)}{q} = \frac{R(q) - C(q)}{q}

In this section, we would want to find the quantity qq, which maximizes profit and average profit. To maximize profit, we would want to solve for:

P(q)=0P'(q) = 0

To maximize average profit, we would want to solve for:

AP(q)=0A P'(q) = 0

  • 1.
    Marginal Profit, and Maximizing Profit & Average Profit Overview:
  • 2.
    Marginal Profit

    Given the following information, find the marginal profit and the value of qq which maximizes the profit. Lastly, calculate the maximum profit.

  • 3.
    Average Profit

    Given the following information, find the marginal average profit and the value of qq which maximizes the average profit:

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Marginal profit, and maximizing profit & average profit

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