Peter's Pipers produces plumbing pipe. The long-run total cost of Peter's pipes is LTC=20000Q-200Q^2+Q^3where Q is measured as thousands of feet of piping and is greater than 0. The long-run marginal cost of Peter's pipes is given as LMC=20000-400Q+3Q^2

a. Divide total cost by Q to obtain Peter's long-run average cost of producing pipe.

b.Exploit the relationship between LMC and LAC to find the quantity where LAC is at a minimum.

c. What is the lowest possible average cost at which Peter can produce pipe?

d.Over what range of output does Peter's Pipers experience economies of scale? Over what range of output does Peter's Pipers experience diseconomies of scale?