A community theater uses the function [tex]p(d)=-4d^{2} +200d-100[/tex] to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at [tex]d[/tex] dollars each.
write and solve an equation to find out the prices at which the theater would earn $1,500 in profit from the comedy show each weekend. show your reasoning.
at what price would the theater make the maximum profit, and what is that maximum profit? show your reasoning.
