For a certain company, the cost function for producing$$x$$items is C$($x$)=50$x$+100$ and the revenue function for selling$$x$$items is$$R$($x$)=0\mathrm{.}5($x$110)2+6,050.$ The maximum capacity of the company is $140$items$.$

$1.$ what is the profit function

$2.$ what is the domain of the profit

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The profit function P$($x$)$is the revenue function R$($x$)($how much it takes in$)$minus the cost function C$($x$)($how much it spends$).$ In economic models, one typically assumes$$that a company wants to maximize its profit, or at least make a profit!