Maximize Profit Example

Business Calculus · Axiom Academy

EXAMPLE Maximize Profit Example Finding the production level that maximizes profit Problem: Furniture Manufacturing Company A furniture company manufactures custom desks. Based on market research: Where x is the number of desks and p is the price per desk in dollars. Find: How many desks should they produce to maximize profit? What is the maximum profit? Substitute the demand function: Take the derivative and set it equal to zero: Use the Second Derivative Test: Since P''(x) = -4 , the function is concave down . Therefore, x = 100 gives a maximum (not a minimum). The company should produce 100 desks and sell them at 300 each to achieve maximum monthly profit of 15,000 . Note: Producing more than 100 desks would require lowering the price too much, reducing overall profit. You've learned the complete process for profit maximization problems. Based on the example above, which approach is correct?

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