1. **State the problem:** We are given the marginal cost function $$MC = 10000 - 20x + x^2$$ and a fixed cost of 9000. We need to find the total cost function $$C(x)$$. 2. **Recall the formula:** The marginal cost $$MC$$ is the derivative of the total cost function $$C(x)$$ with respect to $$x$$, i.e., $$MC = C'(x)$$. 3. **Integrate the marginal cost:** To find $$C(x)$$, integrate $$MC$$ with respect to $$x$$: $$ C(x) = \int (10000 - 20x + x^2) \, dx $$ 4. **Perform the integration:** $$ C(x) = 10000x - 20 \frac{x^2}{2} + \frac{x^3}{3} + C_0 = 10000x - 10x^2 + \frac{x^3}{3} + C_0 $$ 5. **Use the fixed cost:** The fixed cost is the cost when $$x=0$$, so: $$ C(0) = C_0 = 9000 $$ 6. **Write the final cost function:** $$ C(x) = 10000x - 10x^2 + \frac{x^3}{3} + 9000 $$ This function gives the total cost of producing $$x$$ units.