The facilities manager at Oxbridge University is planning to apply fertilizer to the grass in the quadrangle area in the spring. The grass needs nitrogen, phosphorus, and potash in at least the amounts given in the following table:
Mineral __________________ Minimum Weight (lb)
Nitrogen .................................... 12
Phosphorus ................................. 14
Potash ....................................... 18
Three kinds of commercial fertilizer are available, with mineral content and prices per 1,000 pounds as given in the following table. There is virtually unlimited supply of each kind of fertilizer.

How much of each fertilizer should be purchased to satisfy the requirements at minimum cost?

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Phosphorus Content (Ib) Nitrogen Content (Ib) Potash Content (Ib) Price ($) Fertilizer A 10 10 20 10 15 10 5 15