1. Mathematics
2. Linear Transformation
3. Linear Programming
4. 17489

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A brewery manufactures three types of beer - lite, regular, and dark. Each vat of lite beer requires 6 bags of barley, 1 bag of sugar, and 1 bag of hops. Each vat of regular beer requires 4 bags of barlet, 3 bags of sugar and 1 bag of hops. Each vat of dark beer requires 2 bags of barley, 2 bags of sugar and 4 bags of hops. Each day the brewery has 800 bags of barley, 600 bags of sugar, and 300 bags of hops available. The brewery realizes a profit of $10 per vat of lite beer, $20 per vat of regular beer, and $30 per vat of dark beer. How many vats of lite, regular, and dark beer should be brewed in order to maximize profit? What is the maximum profit?