91Ó°ÊÓ

Marginal cost A company manufactures two models of bicycles: a mountain bike and a racing bike. The cost function for producing \(x\) mountain bikes and y racing bikes is given by \(C=10 \sqrt{x y}+149 x+189 y+675\) (a) Find the marginal costs \((\partial C / \partial x \text { and } \partial C / \partial y)\) when \(x=120\) and \(y=160\). (b) When additional production is required, which model of bicycle results in the cost increasing at a higher rate? How can this be determined from the cost model?

Marginal Productivity Consider the Cobb-Douglas production function \(f(x, y)=200 x^{0.7} y^{0.3} .\) When \(x=1000\) and \(y=500,\) find (a) the marginal productivity of labor, \(\partial f / \partial x\) (b) the marginal productivity of capital, \(\partial f / \partial y .\)