Problem

Track the units in \(R(p)=p(100-p)\), where \(p\) is dollars per item and \(100-p\) is the modeled number of items sold. Show how multiplication and unit cancellation determine the units of \(R\).

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p has units of dollars per item and 100 − p has units of items. The operation is multiplication, so p is a unitless exponential multiplier and R has items.

p has units of dollars per item and 100 − p has units of items. Because the factor units differ, they cannot be multiplied and R has no units.

p has units of dollars per item and 100 − p has units of items. The operation adds dollars/item + items, so R has dollars per item plus items.

p has units of dollars per item and 100 − p has units of items. The operation is (dollars/item) · items, so R has dollar units.

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Track the units in \(R(p)=p(100-p)\), where \(p\) is dollars per item and \(100-p\) is the modeled number of items sold. Show how multiplication and unit cancellation determine the units of \(R\).

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