1. The problem is to analyze the marginal cost function $$MC = 15Q - 6Q^2 + 10$$ where $Q$ is the quantity of units produced, and there is a fixed cost of 20. 2. Marginal cost (MC) represents the cost of producing one additional unit. The total cost (TC) function can be found by integrating the MC function and adding the fixed cost. 3. The formula to find total cost from marginal cost is: $$TC = \int MC\, dQ + \text{fixed cost}$$ 4. Integrate the marginal cost function: $$\int (15Q - 6Q^2 + 10) dQ = \frac{15Q^2}{2} - 2Q^3 + 10Q + C$$ 5. Since fixed cost is 20, it acts as the constant of integration $C$: $$TC = \frac{15Q^2}{2} - 2Q^3 + 10Q + 20$$ 6. This total cost function gives the total cost of producing $Q$ units including fixed costs. 7. To summarize: - Marginal cost function: $$MC = 15Q - 6Q^2 + 10$$ - Total cost function: $$TC = \frac{15Q^2}{2} - 2Q^3 + 10Q + 20$$ This completes the solution for the total cost based on the given marginal cost and fixed cost.