1. **State the problem:** We are given a function $f(p)$ representing the number of shoes sold at price $p$. We know $f(120) = 9000$ and $f'(120) = -60$. The revenue function is $R(p) = p \cdot f(p)$. We need to find $R'(120)$ and interpret the effect of a small price increase on revenue. 2. **Formula used:** Revenue is the product of price and quantity sold: $$R(p) = p \cdot f(p)$$ To find the rate of change of revenue with respect to price, use the product rule: $$R'(p) = f(p) + p \cdot f'(p)$$ 3. **Calculate $R'(120)$:** Substitute $p=120$, $f(120)=9000$, and $f'(120)=-60$: $$R'(120) = 9000 + 120 \cdot (-60)$$ 4. **Simplify:** $$R'(120) = 9000 - 7200$$ $$R'(120) = 1800$$ 5. **Interpretation:** Since $R'(120) = 1800 > 0$, a small increase in price near $120$ will increase the manufacturer's revenue. **Final answer:** $$\boxed{R'(120) = 1800}$$ A small price increase will increase revenue.