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∕4K^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.