AVC = 1.24 + .0033Q + .0000029Q2 - .00046QZ - .026Z + .00018Z2 Where AVC = average variable cost (i.e., working costs of generation), measured in pence per kilowatt-hour (kWh). (A pence was a British monetary unit equal, at the time, to 2 cents U.S.) Q = output, measured in millions of kWh per year Z = plant size, measured in thousands of kilowatts a) Determine the long-run variable cost function for electricity generation. b) Determine the long-run marginal cost function for electricity generation. c) Holding plant size constant at 150,000 kilowatts, determine the short-run average variable cost and marginal cost functions for electricity generation. d) For a plant size equal to 150,000 kilowatts, determine the output level that minimizes short-run average variable costs. e) Determine the short-run average variable cost and marginal cost at the out-put level obtained in Part (d).