FTC Applications

Business Calculus · Axiom Academy

Using the Fundamental Theorem to solve business problems 1 Total Cost from Marginal Cost A manufacturing company has marginal cost function: Find the cost of increasing production from 100 to 200 units. The cost of producing units 100 through 200: It costs 6,500 to increase production from 100 to 200 units. This is the variable cost for those 100 additional units (averaging 65 per unit for this production range). A new product generates revenue at the rate: where t is months after launch. Find total revenue in the first 6 months. A city's population grows at the rate: where t is years from now. If current population is 500,000, find population in 10 years. Net Change Formula: Final = Initial + Integral of rate Company A has marginal profit MP_A(x) = 50 - 0.4x Company B has marginal profit MP_B(x) = 30 - 0.1x Which company earns more profit from selling units 10 to 50? Although Company A's marginal profit decreases faster, they start with a higher base profit per unit. For this production range, A is more profitable. At higher quantities, B might overtake A. A stock price over 12 months follows: P(t) = 100 + 20 ( 6 ) Find the average stock price over the year. The sine terms cancel over a complete cycle! Based on the example above, which approach is correct?

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