Answer to Question #309283 in Math for Geki

Question

Consider a Cobb-Douglas production function Q =ALαKβ where the amount produced (Q)

is given as a function of the labor (L) and capital (K) used and A, α, β are constants. Let

the value of the constants in the above production function be given by A = 1, α = 2/3

, β = 1/3

.

Wage rate (w) and per unit capital rate (r) be Rs 4 and Rs 27, respectively. Suppose that

the firm wishes to produce 1080 units of output Q. What will be the optimal amount of

factors that the firm needs to employ for this? Also calculate the minimum cost of

producing such an output level?