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