The total cost function of a firm that produces its product on two assembly lines is given as: subject to the constraint: TC= 3X 2 +6y 2 - XY subject to the constraint: X+Y = 20 The problem facing the...

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, then Find the TC given the values of X and Y.

(C)Interpret the value of the Lagrangian multiplier.