1. **State the problem:** We are given the supply curve $p = 9 + x$ and the quantity sold $x = 7$ units. We need to find the Producer's Surplus. 2. **Formula for Producer's Surplus:** Producer's Surplus is the area above the supply curve and below the market price, up to the quantity sold. It can be calculated as: $$\text{Producer's Surplus} = \text{Total Revenue} - \text{Variable Cost}$$ where Total Revenue = $p \times x$ and Variable Cost is the area under the supply curve from 0 to $x$. 3. **Find the market price at $x=7$:** $$p = 9 + 7 = 16$$ 4. **Calculate Total Revenue:** $$\text{Total Revenue} = p \times x = 16 \times 7 = 112$$ 5. **Calculate Variable Cost:** This is the integral of the supply curve from 0 to 7: $$\int_0^7 (9 + x) \, dx = \int_0^7 9 \, dx + \int_0^7 x \, dx = 9x \Big|_0^7 + \frac{x^2}{2} \Big|_0^7 = 9 \times 7 + \frac{7^2}{2} = 63 + 24.5 = 87.5$$ 6. **Calculate Producer's Surplus:** $$112 - 87.5 = 24.5$$ **Final answer:** The Producer's Surplus is $24.5$ units.