A rm produces gadgets (Q) with only labor (L, measured in worker hours) and capital (K, measured in machine hours). Let w = $10 and r = $30 be the hourly prices of labor and capital, respectively. 1. Assume that labor and capital are perfect substitutes. Each gadget can be produced using either 2 hours of labor and no capital, OR 30 minutes of capital and no labor. a. Write down the rm's production function. b. Use an optimal choice diagram to illustrate the rm's expansion path. 0. Derive the equation for the rm's long-run total cost function. 2. Assume that labor and capital are xed proportion inputs. To produce each gadget the rm must use 2 hours of labor AND 30 minutes of capital. a. Write down the rm's production function. b. Use an optimal choice diagram to illustrate the rm's expansion path. c. Derive the equation for the rm's long-run total cost function