Marginal profit, and maximizing profit & average profit

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Intros
Lessons
  1. Marginal Profit, and Maximizing Profit & Average Profit Overview:
  2. Understanding and Maximizing Marginal Profit
  3. Understanding and Maximizing Average Profit
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Examples
Lessons
  1. Marginal Profit

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

    1. R(q)=2q2+50q+6,C(q)=200+10qR(q) = -2q^{2} + 50q + 6, C(q) = 200 + 10q
    2. R(q)=10q2+10,C(q)=2qR(q) = -\frac{10}{q^{2}} + 10, C(q) = 2q
    3. p(q)=2q+400p(q) = -2q + 400, fixed cost is $200200, costs 4040$ per unit to make
    4. q(p)=(300p)3q(p) = \frac{(300 - p)}{3}, fixed cost is $100100, variable cost is $2q22q^{2}
  2. Average Profit

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

    1. R(q)=q2+35q,C(q)=100+5qR(q) = -q^{2} + 35q, C(q) = 100 + 5q
    2. R(q)=100q+400,C(q)=5qR(q) = -\frac{100}{q} + 400, C(q) = 5q
    3. p(q)=2q+50 p(q) = -2q + 50, fixed cost is $5050, costs $1010 per unit to make
    4. q(p)=400p2q(p) = \frac{400 - p}{2}, fixed cost is $288288, variable cost is $20q20q