# Linear Programming : Find Maximum Profit by Incorporating the Duality

A brewery manufactures 3 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 barley, 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 profits? What is the maximum profit?

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#### Solution Summary

Maximum profit is found by incorporating the duality. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.