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a movie theater has been charging $10 per person and selling about 500 tickets on a typical weeknight. After surveying their customers, the theater estimates that for every 50 cents that they lower the price, the number of moviegoers will increase by 50 per night. Find the demand function and calculate the comsumer surplus when the tickets are $8.
\[(10-x)(500+100x) = 5000+500 x-100 x^2\] So this one is constructed so that you put in the lowering in price and gets the amount of money you make. For example then the price is 8$ the lowering from the original price is 2 so you put 2 into the equation and you get : \[5000+500*(2)-100*(2)^2 = 5600\]