# The quantity, q, of a product manufactured depends on the number of workers, W , and the amount of capital

## Question:

The quantity, q, of a product manufactured depends on the number of workers, W , and the amount of capital invested, K, and is given by the Cobb-Douglas function q = 6W^{3∕4}K^{1∕4}.

In addition, labor costs are $10 per worker and capital costs are $20 per unit and the budget is $3000.

(a) What are the optimum number of workers and the optimum number of units of capital?

(b) Re compute the optimum values of W and K when the budget is increased by $1. Check that increasing the budget by $1 allows the production of λ extra units of the product, where λ is the Lagrange multiplier.

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**Related Book For**

## Applied Calculus

**ISBN:** 9781119275565

6th Edition

**Authors:** Deborah Hughes Hallett, Patti Frazer Lock, Andrew M. Gleason, Daniel E. Flath, Sheldon P. Gordon, David O. Lomen, David Lovelock, William G. McCallum, Brad G. Osgood, Andrew Pasquale

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