The Black Forest Brewery produces four types of beer: pilsner, amber, brown ale

Question

The Black Forest Brewery produces four types of beer: pilsner, amber, brown ale and hefeweizen. The brewery has enough vat capacity to produce 5,000 gallons of beer per month. A gallon of pilsner beer requires 4 pounds of malt extract and 5 ounces of hops, a gallon of amber beer requires 3 lbs. of malt extract and 3.5 ounces of hops, a gallon of brown ale requires 5 pounds of malt extract and 6 ounces of hops, and a gallon of hefeweizen requires 2.5 lbs of malt extract and 3 ounces of hops. The brewery is able to acquire 5 tons of malt extract and 1,000 pounds of hops every month. The largest seller is the pilsner beer, which provides a profit of $26 per gallon. However, the market demands that at least 500 gallons of each type, but not more than 1,300 gallons of brown ale or hefeweizen. The other profits per gallon are $24 for amber, $20.50 for brown ale and $18.50 for hefeweizen. The brewery owner wishes to maximize total profits. a) Define the decision variables, give the objective and constraints in algebraic form. b) Give the data table. c) Use a guess and check approach to find a solution that satisfies the constraints. It does not have to maximize profit.

Explanation / Answer

P = 26a + 24b + 20.5c + 18.5d

(4a + 3b + 5c + 2.5d) pounds <= 5 tons (11023.113 pounds)

(5a + 3.5b + 6c + 3d) ounces <= 1000 pouds (16000 ounces)

a + b + c + d <= 5000

a >= 500
b >= 500
500 <= c <= 1300
500 <= d <= 1300

Maximum P = 26(500) + 24(1257) + 20.5(500) + 18.5(500)
= 62,668 $

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