1. A brewery produces beer and ale. Beer sells for $ 5 per barrel, and ale for $ 2 per barrel. The production of a barrel of beer requires 5 pounds of corn and 2 pounds of hops. The production of a barrel of ale requires 2 pounds of corn and 1 pound of hope. 60 pounds of corn and 25 pounds of hops are available. a) Explain why a Linear Programming (LP) model would be suitable for this case study. [5 marks] b) Formulate a LP model to help the brewer}r management to maximise the revenue while satisfying all constraints. [5 marks] c) Use the graphical method to nd the optimal solution. Show the feasible region and the optimal solution[s] on the graph. Annotate all lines on your graph- What is the optimal daily prot for the factory? Note I: it is possible to have midtiple optimal points. [10 marks] Note 2: yon can use graphical solvers available online hat make S'f'E that your graph is clear, all variables involved are clearly represented and annotated, and each line is clearly marked and related to the corresponding equation. cl) Find the range for the prot ('5), of a barrel of beer (if any}, that can be changed without affecting an optimal point of part (c)? [5 marks]