Problem

A distributor imports olive oil from Spain and Italy in large casks. He then mixes these oils in different proportions to create three grades of olive oil that are sold domestically in the United States. The domestic grades include (a) commercial, which must be no more than 35% Italian; (b) virgin, which may be any mix of the two olive oils; and (c) extra virgin, which must be at least 55% Spanish. The cost to the distributor for Spanish olive oil is $6.50 per gallon. Italian olive oil costs him $5.75 per gallon. The weekly demand for the three types of olive oils is 700 gallons of commercial, 2,200 gallons of virgin, and 1,400 gallons of extra virgin. How should he blend the two olive oils to meet his demand most economically?