please provide detailed answer and explanation thanks

2. (20 marks) Suppose a firm has two different methods of production using the same capital (i.e. same machines). Method 1 will produce using a CES production function: q = h( K, L) = ( VK + VI)2 Method 2 will produce using a Cobb-Douglas production function: q = g(K, L) = 4X VK XL Unless specified otherwise, assume P = $10, w = $20, and r = $5 for the remainder of the question. Use the information about to answer the following questions: (a) (3 marks) What is the optimal level of labour to hire in the short run using h(K, L) given K = 36? (b) (3 marks) What is the optimal level of labour to hire in the short run using g(K, L) given K = 36? (c) (3 marks) How does the firm's profits compare in part (a) versus part (b)? Why? (d) (6 marks) What is the short run cost function using h(K, L)? What about using g(K, L)? Show the optimal q* for both. (e) (5 marks) In the long run, which method would be better for the firm? Explain why. Would your answer remain the same if w =r = $10? Explain. (Hint: what does the long run cost function look like for each? OR how do the Isoquant- Isocost relationships differ?)