Lutz Brewery brews three brands of beers: Lutz Lager, Lutz Light, Lutz Ultralight. Lager sells for $12 per barrel, Light sells for $10 and Ultralight sells for $14 per barrel. Producing a barrel of Lager requires 8 pounds of corn and 4 pounds of hops. Producing a barrel of Light requires 2 pounds of corn, 6 pounds of rice, and 3 pounds of hops. Producing  a barrel of Ultralight requires 1 pounds of corn, 8 pounds of rice, and 2 pounds of hops. The brewery has 5000 pounds of corn, 3000 pounds of rice, and 4000 pounds of hops. To supply demand from established customers, Lutz brewery should produce at least 200 barrels of each product.

a) Assuming a linear relationship, use Excel Solver to determine the optimal mix of Lager, Light and Ultralight that maximizes Lutz Brewery's revenue.

b) Conduct sensitivity analysis and interpret results.