Let x = dollar increase in price Let y = fewer number of pairs sold Since 2 fewer shoes are sold for each 1 dollar (factor of 2) y = 2x Revenue = Number of shoes sold * Price charged per shoe Number of shoes sold = 550 - y = 550 - 2x Price charged per shoe = $99 + $x Revenue = (200 - 2x)(99 + x) = -2x^2 + 550x - 198x + 19800 Revenue = -2x^2 + 352x + 19800 In a quadratic equation, Revenue is maximized when x = -b / 2a. In this case: x - -352 / (2*-2) = $88 Price charged per show = $99 + $x = $99 + $20 = $119. Maximum revenue = -2x^2 + 352x + 19800 (evaluated at x = $88)
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