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 = 200 - y = 200 - 2x
Price charged per shoe = $60 + $x
Revenue = (200 - 2x)(60 + x) = -2x^2 + 200x - 120x + 12000
Revenue = -2x^2 + 80x + 12000
In a quadratic equation, Revenue is maximized when x = -b / 2a. In this case:
x - -80 / (2*-2) = $20
Price charged per show = $60 + $x = $60 + $20 = $80.
Maximum revenue = -2x^2 + 80x + 12000 (evaluated at x = $20)
Maximum revenue = -2(20^2) + 80*20 + 12000 = $12800
