5. Bloomington Breweries produces beer and ale. Beer sells for $25 per barrel, and ale sells for $20 per barrel. Producing a barrel of beer requires 5 lbs. of corn and 2 lbs. of hops. Producing a barrel of ale requires 3 lbs. of corn and 1 lb. of hops. There are 60 lbs. of corn and 22 lbs. of hops available. Formulate the linear programming problem to find the number of barrels of beer and ale that must be produced to maximize the revenue. a. Set-up the Linear Programming Problem (LPP) b. Use graphical and algebraic methods to: a. Solve the LPP b. Perform all of Post-Optimality Analysis, including: i. Slack and surplus variables ii. Sensitivity Analysis, including: 1. Constraint analysis with shadows 2. Price (objective function analysis