Answer: Marginal Revenue A pharmaceutical corporation has two plants that produce the

Chapter 13, Problem 117

(choose chapter or problem)

Marginal Revenue A pharmaceutical corporation has two plants that produce the same over-the-counter medicine. If \(x_{1}\) and \(x_{2}\) are the numbers of units produced at plant 1 and plant 2, respectively, then the total revenue for the product is given by \(R=200 x_{1}+200 x_{2}-4 x_{1}^{2}-8 x_{1} x_{2}-4 x_{2}^{2}\). When \(x_{1}=4\) and \(x_{2}=12\), find (a) the marginal revenue for plant 1, \(\partial R / \partial x_{1}), and (b) the marginal revenue for plant 2, \(\partial R / \partial x_{2}\).

Text Transcription:

x_1

x_2

R=200x_1+200x_2-4x_1^2-8x_1x_2-4x_2^2

x_1=4

x_2=12

partialRpartialx_1

partialRpartialx_2