3. (20%) Consider the production function F(21, Z2) = (21) 4 (22) 2. (a) The production function is indeed concave. Verify that it exhibits strictly de- creasing return to scale and diminishing marginal products. (b) Suppose the good price is p = 2 and factor prices are w1 = 6 and w2 = 1. We now find out the profit-maximizing input bundle for given prices. i. Write down the conditions for the profit-maximizing bundle (21, Z2) ii. Show that it is optimal for the firm to use Z1 = 14. Specifically, you need to find out the profit-maximizing input bundle (21, Z2) and verify that 21 = 1 144 . Hint: You may make use of the information 21 = 144 to simplify your calculation. iii. Find out the firm's profit