Profit Maximization

Business Calculus · Axiom Academy

Using calculus to find the production level that maximizes profit Every business wants to maximize profit. But how do you find the exact quantity to produce? This is where calculus becomes essential. Profit = Revenue - Cost. To maximize it, we use calculus! The quantity q* that makes P(q) as large as possible - the profit-maximizing quantity . To maximize profit, we use the same technique as finding any maximum: set the derivative equal to zero. Marginal Revenue = Marginal Cost Produce until the revenue from one more unit equals the cost of making it. A company has the following revenue and cost functions: Find the profit-maximizing quantity and maximum profit. Visualizing Profit Maximization Where MR = MC, profit is maximized Left of q*: MR > MC, profit still increasing Right of q*: MR < MC, profit decreasing

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