Calculate the Lagrange multiplier of the cost minimization problem with a Cobb-Douglas production function, and show that it is equal to the derivative of the cost function with respect to output (the marginal cost).

The question above is the referral question (providing some insight) to this second one: Let f(x1, x2) = (min{x1 x1, 0})1 (min{x2 x2, 0})2 , where x1, x2 > 0 are interpreted as minimum requirements of inputs needed for the firm to operate, and 1,2 > 0 with 1 +2 = < 1. Draw some isoquants, and obtain the cost function and the conditional demands for inputs. How does it compare to the cost function in section 7?