A brewery produces lager and ale beers. The net profit obtained for a barrel of lager sold is $70 and for a barrel of ale is $30. Producing a barrel of lager requires 5 pounds of corn, 180 grams of yeast, and 2 pounds of hops. Producing a barrel of ale requires 2 pounds of corn, 120 grams of yeast, and 1 pound of hops. The brewery has 60 pounds of corn, 2800 grams of yeast, and 25 pounds of hops. What is the optimal production of each of the beers that maximizes the brewery’s revenue? Assume that you can produce fractions of a barrel.
1. Formulate this problem mathematically (specifying parameters, variables, constraints, and objective function) and solve it in AMPL. Use Gurobi. What is the optimal production plan?
2. Formulate and solve the dual problem in AMPL. Use Gurobi. How can you interpret the optimal solution of the dual problem?