Problem 1: Bloomington Breweries produces beer, ale, lager and a pilsner. Beer sells for $3 per barrel. Ale sells for $4 per barrel. Lager sells for $6 per barrel and Pilsner sells for $4.50 per barrel. The table below shows ingredient requirements (in lbs.) for each barrel of brewery type produced as well as availability of each ingredient. Assume all quantities of Pilsner produced can be sold but no more than 50,000 barrels of each Ale and lager can be sold and at least 30,000 barrels of beer must be sold. Formulate an LP problem to maximize brewery sales and solve

Requirements Ingredient Amount Available (in lbs.) Ale Pilsner er Lager 4 Corn 6 4 700000 Malt 1 2 3 2 500000 Hops 500000 2 3 3 3