Combine standard functions using arithmetic operations to build models.
Form a product function and interpret it in context
Problem
At input \(x\), \(p(x)~=~10~-~x~\text{dollars}~\text{per}~\text{item}\) is price and \(q(x)~=~5x~\text{items}\) is quantity sold. Multiply the functions, simplify the product, and interpret its output.
Big Picture
What this problem is really about
A product function multiplies two outputs produced at the same input. We’ll identify one factor as price per item and the other as item quantity, form their product before expanding, and distribute carefully through the binomial. Tracking units provides a separate check because the item units must cancel to leave the quantity requested by the context.
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