Chapter 7.4, Problem 34E

Productivity. The research department of a manufacturing company arrived at the following Cobb-Douglas production function for a particular product:

     $N\left(x,y\right)=10.x^{0.6}{y}^{0.4}$

In this equation, x is the number of units of labor and y is the number of units of capital required to produce N(x, y) units of the product. Each unit of labor costs $30 and each unit of capital costs $60.

1. (A) If $300,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production, and find the maximum production.
2. (B) Find the marginal productivity of money in this case, and estimate the increase in production if an additional $80,000 is budgeted for the production of the product.