A perfectly competitive firm sells two goods. The price of the first good is $36. The price of the second good is $35. The total cost for the firm is given by the expression:

TC (Q₁, Q₂) = 3Q₁²+2Q₁Q₂+3Q₂²+7Q₂

A. Find the maximum profit and the optimal values of Q₁ and Q₂.

B. If the firm cannot produce in total more than 6 units, then what would be the maximum profit and the optimal values of Q₁ and Q₂? Find your answer using the Lagrange multiplier. Find the value of the Lagrange multiplier. What economic interpretation has the Lagrange multiplier in this context?