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BUS 306 - Management Science - Case 2 Hopping Gnome Brewing Company produces several different types of beer each year. There are a limited amount of grains and hops available each year for purchase to make the beer in 4500-pint batches There is vanous demand for each type of beer produced Hopping Gnome wants to try to maximize the profit while meeting the conditions listed below. The following information is given Light Light Dark Golden Heavy Cost per Heavy (lb, hr, Availability etc) Brew Brew 28 33 20-25 Wheat 15-25 Wheat 8 13 Ale 10 15 Stout 5 - 10 475 500 600 120 500 100 475 250 150 550 200 100 130 130 50 40 150 30,000 8,500 4,000 5,500 5,000 2,500 600 250 60 200 125 100 125 Percent of Demand 2-Row Grain (lb) 6 Row Grain (lb) Crystal Grain (lb) Vienna Grain (b) Barley (b) Malt Extract (lb) Hallertauer Hops (lb) Kent Goldings Hops (lb) Tettnanger Hops (lb) Labor (hr) Average # pints per batch Beer price (per pint) 100 $0.45 $0.38 $0.40 $0.41 $0.43 $0:35 $0.34 $0.31 $0.35 $22.00 40 10 50 40 30 20 10 15 12 11 3 10 10 300 14 12 14 12 600 80 70 75 90 4,000 12 85 4,500 $3.75 60 4,500 $3.45 4,500 $3.50 4,500 $3.00 4,500 $4.10 4,500 $3.20 There are also overhead costs of 58000 per batch of beer. Managerial Report Determine how much batches of each beer Hopping Gnome should produce while meeting demands and maximizing profit. Your report should include the following: a b c Calculate the profit function per batch of each beer. Be sure to consider the costs of each ingredient used and labor costs. Develop and solve an LP model that will help determine how marry batches Hopping Gnome should make of each product to prepare for the next year. Be sure to define your decision variables and write out your objective functie and all of your constraints. In the brewing business, the price and availability of ingredients can vary a lot Examine the effect of a 10 percent decrease in the availability of all of the ingredients on the optimal solution (so your supply of ingredients in 10% less for each one) Due to a small demand in Heavy Stout beer, Hopping Gnome would like to know what would happen if it was removed from production. Remove Heavy Stout Beer from the model and solve the model again. What are the new objective function constraints, and results? Modify your model from part b How much difference is there from your answer in part a concerning how many batches to produce of each? How rouch does it allect profits? Do you recommend removing heavy stout from production Support your answer with mathematical as well as logical evidence d BUS 306 - Management Science - Case 2 Hopping Gnome Brewing Company produces several different types of beer each year. There are a limited amount of grains and hops available each year for purchase to make the beer in 4500-pint batches There is vanous demand for each type of beer produced Hopping Gnome wants to try to maximize the profit while meeting the conditions listed below. The following information is given Light Light Dark Golden Heavy Cost per Heavy (lb, hr, Availability etc) Brew Brew 28 33 20-25 Wheat 15-25 Wheat 8 13 Ale 10 15 Stout 5 - 10 475 500 600 120 500 100 475 250 150 550 200 100 130 130 50 40 150 30,000 8,500 4,000 5,500 5,000 2,500 600 250 60 200 125 100 125 Percent of Demand 2-Row Grain (lb) 6 Row Grain (lb) Crystal Grain (lb) Vienna Grain (b) Barley (b) Malt Extract (lb) Hallertauer Hops (lb) Kent Goldings Hops (lb) Tettnanger Hops (lb) Labor (hr) Average # pints per batch Beer price (per pint) 100 $0.45 $0.38 $0.40 $0.41 $0.43 $0:35 $0.34 $0.31 $0.35 $22.00 40 10 50 40 30 20 10 15 12 11 3 10 10 300 14 12 14 12 600 80 70 75 90 4,000 12 85 4,500 $3.75 60 4,500 $3.45 4,500 $3.50 4,500 $3.00 4,500 $4.10 4,500 $3.20 There are also overhead costs of 58000 per batch of beer. Managerial Report Determine how much batches of each beer Hopping Gnome should produce while meeting demands and maximizing profit. Your report should include the following: a b c Calculate the profit function per batch of each beer. Be sure to consider the costs of each ingredient used and labor costs. Develop and solve an LP model that will help determine how marry batches Hopping Gnome should make of each product to prepare for the next year. Be sure to define your decision variables and write out your objective functie and all of your constraints. In the brewing business, the price and availability of ingredients can vary a lot Examine the effect of a 10 percent decrease in the availability of all of the ingredients on the optimal solution (so your supply of ingredients in 10% less for each one) Due to a small demand in Heavy Stout beer, Hopping Gnome would like to know what would happen if it was removed from production. Remove Heavy Stout Beer from the model and solve the model again. What are the new objective function constraints, and results? Modify your model from part b How much difference is there from your answer in part a concerning how many batches to produce of each? How rouch does it allect profits? Do you recommend removing heavy stout from production Support your answer with mathematical as well as logical evidence d