The Chemistry department at a local college decides to stock at least 900 small test tubes and 600 large test tubes. It wants to buy at least 2700 test tubes to take advantage of a special price. Since the small test tubes are broken twice as often as the large, the department will order at least twice as many small test tubes as large.

a) If the small test tubes cost 18 cents each and the large ones cost 15 cents each, how many of each size should be ordered to minimize cost?

b) Suppose the minimum number of test tubes is increased to 3000. Use shadow costs to calculate the total cost in this case.