A brewery produces two kinds of beer, stout and IPA . Each batch of stout sells for $60 per unit while each batch of IPA sells for $108. Both products require malt, hops, barley, filtered water, and yeast, measured in physical "units" for convenience. Each batch of stout  uses 1 unit of malt, 1 unit of hops, 2 units of barley, 5 units of yeast, and 10 units of filtered water. The corresponding requirements for IPA are: 5 units malt, 2 units hops, 1 unit barley, 8 units yeast and 9 units water. On any given day, the brewery has on hand 150 units of malt, 90 units of hops, and 150 units of barley. The brewery pays $2 per unit for filtered water and $4 per unit of yeast.

1. Solve the problem graphically to determine the daily amounts of stout and IPA that maximize the brewer's profits.
2. State and solve the dual problem using the information you derived for the primal problem.
3. Interpret the dual problem in terms of economics.