Please answer all questions. Question 1 [20 marks] This question refers to the relationship between two optimization problems. @ Profit Maximization Maximize{n = n(L,K)} where: Total Profit - II = II(L, K) = TR - TC Total Revenue - TR = P x Q. Q = f(L. K) - Production function Total Cost - TC = wxL+rxK The solution to this problem requires MRTS = - W # Constrained-cost minimization The objective function is Total Cost - TC= wxl+rxK and the constraint is f ( L. K) = Q* - Prescribed output level The solution to this problem also requires MRTS =The following statement: \"If the firm is maximizing prots, then it is minimizing costs; and vice versa. if the firm is minimizing [31515 if is maximizing profits." consists of two parts: Part 1: Prot maximization cannot exist without cost minimization, and Part 2: Cost minimization cannot exist without prot maximization. One part is true while the other is false. Your Task ( Please reacl carefully if Ignore the part that is true. if Select the part that is false and explain why is false. To gain marlts you hag-jetgjustify your