Answer Happy

Problem 1 • A brewery produces lager, ale, and pilsner beers. The net profits are $71, $35, and $40 for a barrel sold of lager, ale, and pilsner, respectively. Producing a barrel of lager requires 5.5 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. Producing a barrel of pilsner requires 3.5 pounds of corn, 130 grams of yeast, and 1.5 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 are able to sell whole barrels only.
Problem 1 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? Solve the linear relaxation of this problem in AMPL. Report the optimal solution and optimal objective function. Solve the problem step-by-step using Branch and Bound. Solve the problem at every node using AMPL and report the optimal solution and the optimal objective function value. As shown in class, draw a Branch and Bound tree indicating the constraints added, the reasons for pruning, the objective at each node, and the solution obtained. Follow the following rules (depth first search): • After solving the corresponding linear program at a node, always branch on the side first. • Branch on the variable with the smallest index (.e., x; before x; for j>i) • Continue branching on the side if the solution found is fractional. • If a problem on the side is infeasible or the solution found is integer, then solve the pending node of the most recently visited node. ASU
What to upload in Canvas (100 pts)? • A report including • Mathematical formulation • AMPL code and problem solution • Step-by-step solution using Branch and Bound