Maximizing Revenue (Quadratic)

Business Calculus · Axiom Academy

EXAMPLE Maximizing Revenue (Quadratic) A complete worked example of revenue optimization A concert venue can sell tickets at 80 each and sell 1,000 tickets. Market research shows that for every 5 price increase, 50 fewer tickets will be sold. Find: What ticket price maximizes revenue? Let's introduce a variable to represent the price change: Let x = number of 5 price increases If x = 2 (two 5 increases), what is the new price? What type of function is R(x) = -250x^2 + 1000x + 80000 ? Find the Optimal Price Increase For R(x) = -250x^2 + 1000x + 80000 , we identify: Substitute x = 2 into the revenue function: How many tickets are sold at the optimal price of 90? Let's verify by checking revenue at nearby prices: Revenue is maximized at 90, not 80 (original) or higher prices The original revenue was 80 1000 = \ 80,000 Raising the price to 90 increases revenue by 1,000 Going higher than 90 would decrease revenue

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