For this question, assume that the firm has a production function given by f(z1, Z2) = 321 22 Answer the following: Write your answers to 3 decimal places. a) Calculate the TRS between input 1 and input 2. Evaluate it at 21 = 22 = 35 . b) Using the expression for the TRS you found in a) (not its value), apply FOC to find the conditional input demand functions for input 1 and 2. What is the conditional input demand for input 2 when w1 = 8, W2 = 8, q = 19? c) Using the expression for the conditional input demand functions for input 1 and 2 you found in b), find the expression for the cost function c(W1, W2, q) . What is the value of the cost function at w1 = 12, w2 = 7, q = 28? d) Suppose the firm faces some legal constraints of the total output it can produce. Namely, the firm can only produce q E [0, 492] . But its technology, and therefore its cost function, is not affected by this legal restriction. Using the expression for the cost function you found in c), find the maximal output level legally produced at which the average cost and the marginal cost are equalised