Burdell Distilleries in Knoxville is opening a new facility for its whiskey production. There are 3 machines, a, b, and c. Machine a uses 6 pounds of corn, 18 pounds of barley and 6 pounds of rye to produce a batch of 30 bottles of Tennessee whiskey worth $4000. Machine b uses 36 pounds of corn to produce a batch of 45 bottles of Moonshine worth $1500. Machine c uses 21 pounds of rye, 6 pounds of corn, and 3 pounds of barley to produce 30 bottles of Tennessee Rye worth $5400. The distillery has committed to buying at least 1200 pounds of corn per week from local farms. The distillery, however, can only get 2400 pounds of barley and 1800 pounds of rye per week. And storage is limited: there is only room for 10,560 bottles per week of production. For simplicity, we assume that any machine can have its production scaled proportionally by increasing or decreasing the amount of corn, rye and/or barley. What mix of production runs - whiskey, moonshine, and rye - should Burdell use to maximize it's sales for a week?
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