Fertilizing the Lawn. 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:

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?