Example A firm has a production function of the following form, [insert utility function], using labor (L) and capital (K) as inputs. The wage is equal to [insert wage value] and the rental rate of capital is equal to [insert rental rate of capital value]. The firm has a target output equal to [insert target output value] a) Calculate the firm's long-run optimal inputs. b) Graph the optimal inputs, including the isocost curve and isoquant associated with the optimal inputs. c) Now imagine that it is the short run and the firm's capital is fixed at [insert value]. Recalculate the optimal inputs for the short run. d) Draw the short-run optimal inputs and the associated isocost curve on the graph that you drew in part (b) Be sure that you clearly label the short-run and the long-run solution