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Calculus

Power ruleCalculus

Critical number & maximum and minimum valuesCalculus

Demand, revenue, cost & profit- Home
- Business Calculus
- Business Derivative Application

Still Confused?

Try reviewing these fundamentals first

Calculus

Power ruleCalculus

Critical number & maximum and minimum valuesCalculus

Demand, revenue, cost & profitStill Confused?

Try reviewing these fundamentals first

Calculus

Power ruleCalculus

Critical number & maximum and minimum valuesCalculus

Demand, revenue, cost & profitNope, got it.

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Get Started Now- Intro Lesson: a5:50
- Intro Lesson: b6:35
- Lesson: 1a2:37
- Lesson: 1b3:48
- Lesson: 1c4:51
- Lesson: 1d7:22
- Lesson: 2a5:03
- Lesson: 2b5:44
- Lesson: 2c6:17
- Lesson: 2d8:50

Basic Concepts: Power rule, Critical number & maximum and minimum values, Demand, revenue, cost & profit

Related Concepts: Consumer and producer surplus

**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,

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

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

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

- IntroductionMarginal Profit, and Maximizing Profit & Average Profit Overview:a)Understanding and Maximizing Marginal Profitb)Understanding and Maximizing Average Profit
- 1.
**Marginal Profit**Given the following information, find the marginal profit and the value of $q$ which maximizes the profit. Lastly, calculate the maximum profit.

a)$R(q) = -2q^{2} + 50q + 6, C(q) = 200 + 10q$b)$R(q) = -\frac{10}{q^{2}} + 10, C(q) = 2q$c)$p(q) = -2q + 400$, fixed cost is $$200$, costs $40$$ per unit to maked)$q(p) = \frac{(300 - p)}{3}$, fixed cost is $$100$, variable cost is $$2q^{2}$ - 2.
**Average Profit**Given the following information, find the marginal average profit and the value of $q$ which maximizes the average profit:

a)$R(q) = -q^{2} + 35q, C(q) = 100 + 5q$b)$R(q) = -\frac{100}{q} + 400, C(q) = 5q$c)$p(q) = -2q + 50$, fixed cost is $$50$, costs $$10$ per unit to maked)$q(p) = \frac{400 - p}{2}$, fixed cost is $$288$, variable cost is $$20q$