Suppose a firm's production function is characterized by , 100//. Wages are w = $25 and capital has a price/machine hour r = $80. Capital is fixed at . a. (8 Points) Derive the short-run average and marginal cost functions SAC and SMC. Show all steps as usual. These will naturally be functions of . b. (6 Points) Derive the quantity level that minimizes SAC. This too will be a function of . c. (6 Points) Derive the long-run TC, AC and MC curves. Show all steps. d. (6 Points) Let = 10, 20, 40. Plot the SAC's and AC with q on the X-axis, $ on the Y axis. Annotate the graph clearly. At which q does SAC = AC for each ?