Minimum Average Cost

Business Calculus · Axiom Academy

Finding the most efficient production level Problem: Furniture Manufacturer A furniture company has the following total cost function for producing chairs: The production level that minimizes average cost Divide total cost by quantity: To minimize AC, take its derivative and set equal to zero: Set the derivative equal to zero: Substitute x = 100 into the average cost function: Minimum average cost per chair Recall: MC = AC at Minimum Average Cost Let's verify this relationship: Find the marginal cost function: At x = 100: MC = 40 and AC = 40 This confirms x = 100 is indeed the minimum of the average cost curve. At 100 chairs per day, the company achieves its efficient scale - the lowest possible cost per unit. Producing fewer chairs means high fixed costs per unit; producing more leads to diminishing returns. Optimal production: 100 chairs/day Minimum average cost: 40/chair Total daily cost: C(100) = 4,000 You've learned to find the efficient scale using calculus. Based on the example above, which approach is correct?

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