The total cost function of a firm that produces its product on two assembly lines is given as:

=+

subject to the constraint: +=

The problem facing the firm is to determine the least-cost combination of output on assembly lines X and Y subject to the side condition that total output equal 20 units.

(A) Use the Lagrangian multiplier method to determine X and Y that lead to the minimization of TC.

(B) Verify that the values of X and Y minimize the TC.

(C) Find the TC given the values of X and Y.

(D) Interpret the value of the Lagrangian multiplier.