Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Build a quadratic revenue or profit function from a price-and-demand context
Problem
Price is \(p~\text{dollars}~\text{per}~\text{item}\) and demand is \(Q(p)=80-p\) items. Form revenue as price times quantity, write factored and expanded quadratic forms, explain the resulting dollar units, and give the feasible price interval.
Big Picture
What this problem is really about
Revenue multiplies price per item by the number of items sold, so the demand expression must become a factor rather than an addend. We’ll form and expand that product, track how item units cancel to dollars, and require both price and modeled demand to be nonnegative when finding the feasible interval.
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