Problem

Use the displayed diagrams to analyze \(R=p(50-p)\) for \(0\le~p\le~50\). Interpret price and demand factors with units, derive revenue units, find both zeros, and explain their zero-revenue meanings.

Source revenue graph for R=p(50−p): p is price in dollars per item, 50−p is demand in items, and 0≤p≤50; no zero interpretation is shown.

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Factor p is price in dollars per item and 50 − p is quantity demanded in items; their product is revenue in dollars. For 0 ≤ p ≤ 50, zeros p = 0 and p = 50 give zero modeled revenue.

Factor p is price and 50 − p is demand; their product is revenue. The zero p = 50 is selected as the maximum-revenue price because it makes the demand factor zero.

Factor p is price and 50 − p is demand; their product is revenue. The zero p = 0 is rejected as algebraically invalid even though it is within the stated price domain.

Factor p has dollars per item and 50 − p has items; their operation adds the units, so R has dollars per item plus items. Zeros p = 0 and 50 are both price units.

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Use the displayed diagrams to analyze \(R=p(50-p)\) for \(0\le~p\le~50\). Interpret price and demand factors with units, derive revenue units, find both zeros, and explain their zero-revenue meanings.

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