1. **Problem Statement:** Find the Marshallian demand functions given a consumer's utility maximization problem with a budget constraint. 2. **General Setup:** The Marshallian demand functions are derived by maximizing utility $U(x_1,x_2)$ subject to the budget constraint $p_1x_1 + p_2x_2 = m$, where $p_1, p_2$ are prices and $m$ is income. 3. **Method:** Use the Lagrangian method: $$\mathcal{L} = U(x_1,x_2) - \lambda (p_1x_1 + p_2x_2 - m)$$ 4. **First Order Conditions:** $$\frac{\partial \mathcal{L}}{\partial x_1} = \frac{\partial U}{\partial x_1} - \lambda p_1 = 0$$ $$\frac{\partial \mathcal{L}}{\partial x_2} = \frac{\partial U}{\partial x_2} - \lambda p_2 = 0$$ $$p_1x_1 + p_2x_2 = m$$ 5. **Solve for $x_1$ and $x_2$:** From the first two equations, $$\frac{\partial U/\partial x_1}{\partial U/\partial x_2} = \frac{p_1}{p_2}$$ Use this to express $x_2$ in terms of $x_1$, then substitute into the budget constraint to solve for $x_1$ and $x_2$. 6. **Result:** The solutions $x_1^*(p_1,p_2,m)$ and $x_2^*(p_1,p_2,m)$ are the Marshallian demand functions. Without a specific utility function, this is the general approach to find the Marshallian demands.