Find long-run variable cost function-electricity generation

Question

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+.0033Q + .0000029Q² - .000046QZ - .026Z +.00018Z²

 Where ACV= average variable cost (i.e. working costs of generation) measured in pence per kilowatt-hour (kWh). (A pence was British monetary unit equal, at that time to 2 cent U.S)

Q= output, measured in millions of kWh per year

Z= plant size, measured in thousands of kilowatts

1. Determine the long- run variable cost function for electricity generation
2. Determine the long-run marginal cost function for electricity generation
3. Holding plant size constant at 150,000 kilowatts, determine the short-run average variable cost and marginal cost function for electricity generation
4. For a plant size equal to 150,000 kilowatts, determine the output level that minimizes short-run average variable costs
5. Determine the short-run average variable  cost and marginal cost at the output level obtained in part (d)