C-Town brewery brews two beers: Expansion Draft and Burning River. Expansion Dra

Question

C-Town brewery brews two beers: Expansion Draft and Burning River. Expansion Draft sells for $20 a barrel, while Burning river sells for $8 a barrel. Producing a barrel of Expansion Draft requires 8 pounds of corn, and 4 pounds of hops. Producing a barrel of Burning River requires 2 pounds of corn, 6 pounds of rice, and 3 pounds of hops. The brewery has 500 pounds of corn, 300 pounds of rice, and 400 pounds of hops. Assuming a linear relationship, determine the optimal mix of Expansion Draft and Burning River that maximizes C-Town Brewery revenue.

Explanation / Answer

I think it's 50 barrels of each. I started producing all the $20 E.D. barrels I could, which is 62.5 (lower of 500lbs/corn divided by 8lbs corn/barrel = 62.5, or 400lbs hops divided by 4lbs hops/barrel). Then noted that 8lbs of corn ($20 of E.D.) can be used to produce 4 barrels or (4 x $8) $32 of revenue. So corn is more profitable in B.R. barrels. Rice is the limiting ingredient of B.R. barrels, I can produce a max of 50 barrels with all 300lbs (300 divided by 6), which would leave me with 400lbs of corn [500 to start minus (50barrels x 2lbs corn/barrel)] and 250lbs of hops. With 400lbs of corn I can produce 50 barrels of E.D. and am left with just hops (50lbs). 50 barrels of $20 E.D. nets me $1000, and 50 barrels of $8 B.R. nets me $400, Gross is $1400.

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