A company manufactures 2 models of MP3 players. Let \( x \) represent the number (in millions) of the first model made, and let \( y \) represent the number (in millions) of the second model made. The company's revenue can be modeled by the equation \( R(x, y)=180 x+160 y-4 x^{2}-3 y^{2}-x y \) Find the marginal revenue equations \( R_{x}(x, y)= \) \( R_{y}(x, y)= \)

To find the marginal revenue equations, we take the partial derivatives of the revenue function \( R(x, y) \) with respect to \( x \) and \( y \). 1. **Marginal Revenue with respect to \( x \)**: \[ R_{x}(x, y) = \frac{\partial R}{\partial x} = 180 - 8x - y \] This equation tells you how the revenue changes when you produce one more million units of the first model, while keeping the production of the second model constant. 2. **Marginal Revenue with respect to \( y \)**: \[ R_{y}(x, y) = \frac{\partial R}{\partial y} = 160 - 6y - x \] This equation indicates how the revenue shifts when you increase the production of the second model by one million, with the first model's production held steady.