Frosty Queen Creamery is looking for fresh milk suppliers for its four different plants. The company...

 

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Frosty Queen Creamery is looking for fresh milk suppliers for its four different plants. The company considers bids from five farms. The bids, maximum daily supplies available from each bidder, and the daily demand for each plant are summarized in the following table Plant- bids (8 per gallon) 1 2 3 3.50 4.60 3.65 2.75 4 Farm 1 Farm 2 2.50 2.50 3.20 4.70 Farm 3 2.55 3.20 2.70 4.50 Farm 45.00 4.70 3.60 2.90 Farm 5 2.35 3.95 2.95 3.00 Milk req. (gallons) 100 150 70 120 The following additional requirements need to be taken into account: 1. Farm 1 will only supply Plant 2 if it orders at least 50 gallons of milk. 2. Farm 2 wants the total amount it supplies to all plants to be a multiple of 60 gallons. 3. Farm 3 is only interested working with Frosty Queen Creamery if it orders all the 150 gallons the farm can supply. 4. Farm 4 requires that if it supplies less than 40 gallons to Plant 4, then it must supply at least 40 gallons to Plant 3. 5. Farm 5 insists that at least one of the following conditions is satisfied • supply to Plant 1 is at least 40 gallons • supply to Plant 2 is exactly 80 gallons; • supply to Plant 3 is at most 50 gallons. Formulate the problem of minimizing the daily cost of milk supplies while satisfying all the requirements as an MIP. Implement and solve your model in AMPL. Report your solution below. Gallons of milk supplied daily from each farm to each plant Plant-> Farm 1 Farm 2 Farm 3 Farm 4 Farm 5 Optimal daily cost: S max supply (gallons) 120 180 150 100 80 1 2 3 Frosty Queen Creamery is looking for fresh milk suppliers for its four different plants. The company considers bids from five farms. The bids, maximum daily supplies available from each bidder, and the daily demand for each plant are summarized in the following table Plant- bids (8 per gallon) 1 2 3 3.50 4.60 3.65 2.75 4 Farm 1 Farm 2 2.50 2.50 3.20 4.70 Farm 3 2.55 3.20 2.70 4.50 Farm 45.00 4.70 3.60 2.90 Farm 5 2.35 3.95 2.95 3.00 Milk req. (gallons) 100 150 70 120 The following additional requirements need to be taken into account: 1. Farm 1 will only supply Plant 2 if it orders at least 50 gallons of milk. 2. Farm 2 wants the total amount it supplies to all plants to be a multiple of 60 gallons. 3. Farm 3 is only interested working with Frosty Queen Creamery if it orders all the 150 gallons the farm can supply. 4. Farm 4 requires that if it supplies less than 40 gallons to Plant 4, then it must supply at least 40 gallons to Plant 3. 5. Farm 5 insists that at least one of the following conditions is satisfied • supply to Plant 1 is at least 40 gallons • supply to Plant 2 is exactly 80 gallons; • supply to Plant 3 is at most 50 gallons. Formulate the problem of minimizing the daily cost of milk supplies while satisfying all the requirements as an MIP. Implement and solve your model in AMPL. Report your solution below. Gallons of milk supplied daily from each farm to each plant Plant-> Farm 1 Farm 2 Farm 3 Farm 4 Farm 5 Optimal daily cost: S max supply (gallons) 120 180 150 100 80 1 2 3

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