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Cost, revenue, profit Marginals for linear functions Break Even points Supply and Demand Equilibrium Applications with Linear Functions

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Cost, Revenue, Profit, Marginals Cost: C(x) = variable costs + fixed costs Revenue: R(x) = (price)(# sold) Profit: P(x) = C(x) – R(x) Marginals: what would happen if one more item were produced (for marginal cost) and sold (for marginal revenue or marginal profit)

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Example 1 Find C(50), R(50), P(50) and interpret. Find all marginals when x = 50 and interpret.

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Example 1 – continued Find all marginals when x = 50 and interpret. For linear functions, the marginals are the slopes of the lines.

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Break Even Points Companies break even when costs = revenues or when profit = 0. Example 2

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If P(10) = -150 and P(50) = 450, how many units are needed to break even if the profit function is linear? Example 3 The company breaks even by producing and selling

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Law of Demand: quantity demanded goes up as price goes down. Likewise, as price goes up, quantity demanded goes down. Law of Supply: quantity supplied goes up as price goes up. Likewise, as price goes down, quantity supplied goes down. Market Equilibrium: where quantity demanded equals quantity supplied

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Example 4 Demand: Supply:

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