A study of the costs of electricity generation for a sample of 56 British firms in 1946-1947 yielded the following long-run cost function: AVC = 1.24 + .003Q + .0000029Q^2 - .000046QZ - .026Z + .00018Z^2 where AVC = average variable cost measured in pence per kilowatt-hour. (A pence was a British monetary unit equal, at that 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 output level obtained in Part (D).