Marginal cost, and minimizing cost & average cost

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Introduction
Lessons
  1. Marginal Cost, and Maximizing Cost & Average Cost Overview:
  2. Understanding and Minimizing Marginal Cost
  3. Understanding and Minimizing Average Cost
Examples
Lessons
  1. Finding & Minimizing the Cost
    Given the following information, find the marginal cost and the value of qq which minimizes the cost:
    1. C(q)=20+70q2 C(q)=20+70q^2
    2. C(q)=250+(1+q)(q10)2 C(q)=250+(1+q) (q-10)^2
    3. The fixed cost is $50000, and the cost to make each unit is $500
    4. The fixed cost is $25000, and the variable cost is $200q2q^2.
  2. Finding & Minimizing the Average Cost
    Given the following information, find the marginal average cost and the value of qq which minimizes the average cost:
    1. C(q)=q42q2+10q C(q)=q^4-2q^2+10q
    2. C(q)=100+q2 C(q)=100+q^2
    3. C(q)=q34q2+10q C(q)=q^3-4q^2+10q
    4. C(q)=2q C(q)=2q
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Topic Notes
Marginal Cost (MC) is the additional cost that is gained when you increase the unit by one. It is also the derivative of the cost function. In other words,
MC=C(q)MC=C'(q)

Average Cost (AC) is the amount of cost generated per unit. In other words,
AC(q)=C(q)qAC(q)=\frac{C(q)}{q}
In this section, we would want to find the quantity qq, which minimizes cost and average cost. To minimize cost, we would want to solve for:

MC=0MC=0

To minimize average cost, we would want to solve for:

AC(q)=0AC'(q)=0