4. A firm uses two inputs and 2 to produce output y. The production function is given by f(x1, 72)=min (2x1, 22). The price of input 1 is 1 and the price of input 2 is 2. The price of output is 10. (a) Calculate Marginal Products for each input. Are they increasing or decreasing? (b) Calculate Marginal Rate of Technical Substitution. Is it increasing or diminishing? (c) Draw two or more isoquants (Your drawing may not be exact, but it needs to display the key features of technology such as convexity/concavity accurately). (d) Does this production function exhibit increasing, decreasing or constant returns to scale? (e) Solve the firm's cost minimization problem. Derive the firm's cost function c(y). (f) Find the profit maximizing choice of inputs i and x and output y*. Calculate the firm's profit from these choices.