During the 2002 Winter Olympics in Salt Lake City, Utah, a local microbrewery received a rush order for 100 gallons of beer containing at least 4.0 volume \(\%\) alcohol. Although no \(4 \%\) beer was in stock, large quantities of Beer A with \(4.5 \%\) alcohol at a price of \(\$ 6.40 /\) gallon and Beer B with \(3.7 \%\) alcohol priced at \(\$ 5.00 /\) gallon were available as was water suitable for adding to the blend at no cost. The brewery manager wanted to use at least 10 gallons of Beer A. Neglecting any volume change due to mixing, set up a suitable LP and solve it to determine the volumes (in gallons) of Beer A, Beer B, and water that should be blended to produce the desired order at the minimum cost.