Consider the following production function: q(L,K) = 9 L^1/3 K^1/3, where q is output and the two inputs are K, capital and L, labor. The...

Consider the following production function:

q(L,K) = 9 L^1/3 K^1/3,

where q is output and the two inputs are K, capital and L, labor.

The corresponding cost equation is:

C(L,K) =wL + rK,

where w is the wage and r the opportunity cost of capital.

The Lagragian for the cost minimization problem is:

L = wL + rK + lamda