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