# Exam 1 Fall 2010_11wAnswers - University of Pittsburgh...

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1. Froshinsloth Brewers (20 points) Consider the situation of Froshinsloth Brewers whose two products, Pale Stale Ale, and Logger's Lager, are made from different proportions of barley, hops and malt. Suppose that 480 pounds of barley, 160 ounces of hops, and 1190 pounds of malt are immediately available and that the output is limited by the scarcity of these raw materials. Other resources, such as water, yeast, labor and energy, may be consumed in the manufacturing process, but they are considered to be plentiful. Although they may influence the brewer's willingness to produce the Ale and Lager because of their costs, they do not directly limit the ability to produce. Assume that the brewing of each barrel of Pale Stale Ale consumes five pounds of barley, four ounces of hops, and 35 pounds of malt, whereas each barrel of Logger's Lager requires 15 pounds of barley, four ounces of hops and 20 pounds of malt. As a result of a successful ad campaign based on a catchy slogan ("Beer is proof that God loves us and wants us to be happy.” - Benjamin Franklin), Froshinsloth can sell at current prices all the Ale and Lager that it can produce. A cost study has established that the company will make a profit of \$13 per barrel of Ale and \$23 per barrel of Lager. Model the problem as a linear optimization problem. Please be sure to define your decision variables.
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Exam 1 Fall 2010_11wAnswers - University of Pittsburgh...

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