Chapter 8.6, Problem 25P

To determine

(a)

To calculate:

The optimum number of the workers and optimum number of the capital if the quantity q, of a product manufactured is given by the Cobb-Douglas function $q=6W^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{K}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$ defined in terms of the workers W and the total amount of the capital invested K. The labor cost is $\$10$ per worker and the capital cost is $\$20$ per unit. The total budget available is $\$3,000$.

To determine

(b)

To calculate:

Re-computation of the optimal values of worker and the capital input when the budget is increased by $\$1$ also find the value of $\lambda$ if the quantity q, of a product manufactured is given by the Cobb-Douglas function $q=6W^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}{K}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$ defined in terms of the workers W and the total amount of the capital invested K. The labor cost is $\$10$ per worker and the capital cost is $\$20$ per unit. The total budget available is $\$3,000$.