Directions: the Honest Pint Brewery has engaged your services as a business consultant. You've been asked to assess potential production models for the brewery and to provide a suggested production strategy to maximize monthly profits. Use the data provided below to perform your analysis Your write up of this problem must include two components: first, a business letter addressed to the owners of HPB (Bob and Doug McKenzie, brothers) which outlines the optimal production strategy and addresses the owners concern raised in Question 3. Second, a formal presentation of the model solved using the 5-step method needs to be included as an appendix to the letter. For this mini project, both the letter and solution should be typeset. Make sure your submission is free of spelling and grammatical error The Honest Pint Brewery HPB sells three craft beers by the 160 bottle. The boots are IPA, Inger, and a stout. To make beer, water, maltod barley, hops, and yeast are used in different proportions depending on the particular variety. For a l gallon yield, the following amounts are required: IPA Lager Stout Water (gal) 1 INO 1.106 1.280 Malted Barley (1) 2.2) 1.393 2.273 Hop (Ibs) 0.03 0.011 0.023 Brewer'a semut (kg) 0.167 0.18 0.182 Yield trials) 1.000 1.00 1.000 Note that the recipes cade linearly for 100 lions of IPA, 100 x 1180- 118 gallons of water would be required) Diferent amounts of labor time and fermentation time are loquired for each variety Labor (hru/batch 20 Stout 16, whatch in 100 calotul only the time Once bat has been redan tertented can be botted and sold Estimated one per lloni gallon is: IPA Lager Stout Revenue (S/gal) 36.00 24.00 37.50 Mini Project 2 MAT 488 Seminar in Mathematical Modeling Spring 2021 The costs associated with the brewing process, as well as the wailability of the necessary retources, are detailed below: Coat Availability Water (gal) S 15 2001 gals/month Malted Barley (lb) $2.50 1400 lb/month Hope (15) $ 3.75 50 lbs/month Brewer's Yeast (pkg) $ 6.00 150 pkgs/month Labor (hour) S10.00 320 hours/month Fermentation storaggal NA 1000 cals/month 1. HPB currently produces 1 batch of IPA, 4 batches of lager, and 2 batches of stout each month. However, HPB feels that it can do better. What production plan maximizes monthly profit? Use a linear programming model to answer this question. 2. Determine the shadow price of any binding constraint discovered by your model. 3. The Three Dogs Brewery down the road usually has a surplus of harley at the end of each month. They've asked whether or not HPB would be interested in purchasing the surplus under the following conditions if HPB agrees to buy ALL 600 pounds of their surplus at $7.50 per pound, they will throw in another 5 packages of yeast as well. Is this deal worth it? Directions: the Honest Pint Brewery has engaged your services as a business consultant. You've been asked to assess potential production models for the brewery and to provide a suggested production strategy to maximize monthly profits. Use the data provided below to perform your analysis Your write up of this problem must include two components: first, a business letter addressed to the owners of HPB (Bob and Doug McKenzie, brothers) which outlines the optimal production strategy and addresses the owners concern raised in Question 3. Second, a formal presentation of the model solved using the 5-step method needs to be included as an appendix to the letter. For this mini project, both the letter and solution should be typeset. Make sure your submission is free of spelling and grammatical error The Honest Pint Brewery HPB sells three craft beers by the 160 bottle. The boots are IPA, Inger, and a stout. To make beer, water, maltod barley, hops, and yeast are used in different proportions depending on the particular variety. For a l gallon yield, the following amounts are required: IPA Lager Stout Water (gal) 1 INO 1.106 1.280 Malted Barley (1) 2.2) 1.393 2.273 Hop (Ibs) 0.03 0.011 0.023 Brewer'a semut (kg) 0.167 0.18 0.182 Yield trials) 1.000 1.00 1.000 Note that the recipes cade linearly for 100 lions of IPA, 100 x 1180- 118 gallons of water would be required) Diferent amounts of labor time and fermentation time are loquired for each variety Labor (hru/batch 20 Stout 16, whatch in 100 calotul only the time Once bat has been redan tertented can be botted and sold Estimated one per lloni gallon is: IPA Lager Stout Revenue (S/gal) 36.00 24.00 37.50 Mini Project 2 MAT 488 Seminar in Mathematical Modeling Spring 2021 The costs associated with the brewing process, as well as the wailability of the necessary retources, are detailed below: Coat Availability Water (gal) S 15 2001 gals/month Malted Barley (lb) $2.50 1400 lb/month Hope (15) $ 3.75 50 lbs/month Brewer's Yeast (pkg) $ 6.00 150 pkgs/month Labor (hour) S10.00 320 hours/month Fermentation storaggal NA 1000 cals/month 1. HPB currently produces 1 batch of IPA, 4 batches of lager, and 2 batches of stout each month. However, HPB feels that it can do better. What production plan maximizes monthly profit? Use a linear programming model to answer this question. 2. Determine the shadow price of any binding constraint discovered by your model. 3. The Three Dogs Brewery down the road usually has a surplus of harley at the end of each month. They've asked whether or not HPB would be interested in purchasing the surplus under the following conditions if HPB agrees to buy ALL 600 pounds of their surplus at $7.50 per pound, they will throw in another 5 packages of yeast as well. Is this deal worth it