O.J. Juice Company sells bags of oranges and cartons of orange juice. Oranges are purchased from different suppliers and then transported to O.J.'s warehouses. At the warehouses, the oranges are sorted (separated according to grades) before they are transported to O.J.'s factory. The production process is illustrated in the graph below.

O.J. grades oranges on a scale of 1(poor) to 10(excellent). The oranges from a supplier is a mix of all grades with known percentages. Each supplier cannot provide more than its capacity. The capacity, cost and grade mix of the oranges purchased from a supplier are given as an example in the Table below.

Home Tools Week 7... A-06-20... LinAlg_... tut-probl... tps-05-2... test-pro... 37141Le... 37141Le... 37141-a... * Sign In 2.14 A n o 95.2% do Share E Search OCR Problem O.J. Juice Company sells bags of oranges and cartons of orange juice. Oranges are purchased from different suppliers, and then transported to 0.J.'s warehouses. At the warehouses, the oranges are sorted (separated according to grades) before they are transported to 0.J.'s factory. The production process is illustrated in the graph below. . Export PDF suppliers Po Create PDF Edit PDF transportation = Comment Warehouses - - Combine Files After sorting Fl Organize Pages G3 G4 G5 G 10 G 10 G3 G4 G5 GS UITG 10 Redact G3 G4 G5 transportation 0 Protect Compress PDF Processing plant Cu Fill & Sign Send for Review 0.J. grades oranges on a scale of 1(poor) to 10(excellent). The oranges from a supplier is a mix of all grades with known percentages. Each supplier cannot provide more than its capacity. The capacity, cost and grade mix of the oranges purchased from a supplier are given as an example in the Table below. More Tools Supplier A capacity 2000 Cost $/lb 0. 9 grade 3(%) 5 grade 6 grade 8 2050 grade 10 25 Create, edit and sign PDF forms & agreements According to this Table, Supplier A cannot provide more than 2,000 lb of oranges; if O.J. purchase 1,000 lb oranges from supplier A, after sorting (separating the oranges according to grade), O.J. can have 50 lb oranges of grade 3, 200 lb of grade 6, 500 lb of grade 8 and 250 lb of grade 10. Start Free Trial Week 7... A-06-20... LinAlg_... tut-probl... tps-05-2... test-pro... 37141Le... 37141Le... 37141-a... x @ Sign In Home A Tools CD @ Q 3.14 A n o 95.2% T de Share The purchased oranges are transported from suppliers to 0.J's warehouses. The transportation cost per lb is shown as an example in the Table below supplier1 supplier2 supplier3 Shipping cost($ per lb) Warehouse A Warehouse B Warehouse C 0.10 0.15 0.05 0.25 0.09 0.12 0.12 0.10 The sorting process takes place in 0.J's different warehouses at different cost rate. The amount of oranges sorted by each warehouse must be within its capacity. The sorted oranges are transported to OJ's plant to produce orange juice and bag of oranges. The average quality of oranges sold in bags must be at least 6, and the average quality of the oranges used to produce orange juice must be at least 7.5. The average quality is calculated as the weighted average of the grades of oranges blended together. For example, the average quality of blending 2 lb of grade 2 oranges and 5 lb of grade 9 oranges is 2 x 2 +9 x 5 2+5 The transportation cost from warehouse to plant is $0.05 per lb. Each lb of orange can yield 0.95 lb of bags of orange at a cost of $0.1, while each lb of orange can yield only 0.6 lb of orange juice at a cost of $0.4. The orange juice can be sold at $3.5 per lb, and the bag of oranges is sold at $1.5 a pound. O.J.'s plant can process no more than 30,000 lb of oranges, and must produce at least 3000 lb of bags of oranges. Oranges not used must be sent to a recycling centre at the cost of $0.1 per lb. 0.J. needs to find the optimal production and shipping plan to maximise profit. The detailed data can be found in the Excel file with the name 2020Assign- mentData.xlsx. Questions 1 Investigate how to solve 0.J.'s problem with Linear Programming 2 0.J. is considering to build a new plant. Discuss what data is required for assessing this strategic decision. ASSESSMENT TASKS: AutoSave OFF HE S U 2020AssignmentData Home Insert Draw Page Layout Formulas Data Review Share Comments Get Add-ins View Tell me h-Bv Nu Recommended vs Charts A Slicer Timeline A Av v TT Equation v IT Equation Pivot Recommended Table Table Pivot Tables Pictures Shapes Icons - My Add-ins Maps Pivot Chart Sparklines 5 Link New Comment Text Header & a Box Footer Symbol H I J K L M N O P Q Orange grade grade 7 (%) grade 4 (%) grade 5 (%) grade 6(%) grade 8(%) grade 9(%) grade 10(%) 5 0.3 G78 - XVfx Data for the assignment problem 2 Orange suppliers Purchase Supplier capacity(lb) Cost ($/b) grade 3 (%) 4000 5000 0.2 9000 6000 0.25 3000 0.15 5500 4500 0.18 12 5000 0.22 13 7000 0.25 3500 0.3 0.2 MIN 0.22 15 16 Transportation cost from supplier to warehouse ($/1b) warehouses 19 Supplier 20 22 23 5 0.14 0.06 0.14 0.09 0.09 0.11 0.15 0.11 0.13 0.1 0.15 0.1 0.12 0.1 0.07 0.12 0.05 0.05 0.09 0.11 0.13 0.1 0.05 0.06 0.15 0.1 0.14 0.12 0.13 29 0.13 31 Sorting at warehouses 32 33 warehouses 34 35 capacity (lb) 36 sorting cost ($/lb) 15000 0.12 20000 0.1 20000 0.11 37 38 Transporation cost from warehouses to plant ($/lb) 0.05 39 40 Processing at the plant 41 42 43 Average Quality Rate Products orange juice bag of orange + @ 0 - - + 100% AutoSave OFF HE S U 2020AssignmentData Home Insert Draw Page Layout Formulas Data Review Share Comments Get Add-ins View Tell me h-Bv Nu Recommended Charts the Slicer e A A Av TT Equation Pivot Recommended Table Table Pivot Tables Pictures Shapes Icons - My Add-ins Maps Pivot Chart Sparklines 5 Timeline Link New Comment Text Header & a Box Footer Symbol G78 X v fx L M N O P 10 11 5500 4500 5000 7000 3500 0.22 0.18 0.22 0.25 do BODO 12 13 14 0.3 16 Transportation cost from supplier to warehouse ($/1b) 17 warehouses 18 19 Supplier 20 0.1 0.15 0.14 0.06 0.14 0.09 0.09 0.11 0.15 0.11 0.13 0.13 0.12 0.1 0.07 0.12 0.05 0.05 0.09 0.11 0.13 0.1 0.05 0.06 0.15 0.1 0.14 0.12 0.13 31 Sorting at warehouses warehouses 33 34 35 36 capacity (lb) sorting cost ($/lb) 15000 0.12 20000 0.1 20000 0.11 37 0.05 42 38 Transporation cost from warehouses to plant ($/1b) 39 40 Processing at the plant 41 Products bag of orange orange juice 43 Average Quality 44 Yield 0.95 45 processing cost ($/1b) 0.1 46 selling price ($/lb) 47 minimum production 3000 0.6 1.5 0.4 3.5 49 processing capacity at the plant(lb) 30000 0.1 51 recycling cost (S/1b) 52 53 Rate + @ 0 - - - + 100% Home Tools Week 7... A-06-20... LinAlg_... tut-probl... tps-05-2... test-pro... 37141Le... 37141Le... 37141-a... * Sign In 2.14 A n o 95.2% do Share E Search OCR Problem O.J. Juice Company sells bags of oranges and cartons of orange juice. Oranges are purchased from different suppliers, and then transported to 0.J.'s warehouses. At the warehouses, the oranges are sorted (separated according to grades) before they are transported to 0.J.'s factory. The production process is illustrated in the graph below. . Export PDF suppliers Po Create PDF Edit PDF transportation = Comment Warehouses - - Combine Files After sorting Fl Organize Pages G3 G4 G5 G 10 G 10 G3 G4 G5 GS UITG 10 Redact G3 G4 G5 transportation 0 Protect Compress PDF Processing plant Cu Fill & Sign Send for Review 0.J. grades oranges on a scale of 1(poor) to 10(excellent). The oranges from a supplier is a mix of all grades with known percentages. Each supplier cannot provide more than its capacity. The capacity, cost and grade mix of the oranges purchased from a supplier are given as an example in the Table below. More Tools Supplier A capacity 2000 Cost $/lb 0. 9 grade 3(%) 5 grade 6 grade 8 2050 grade 10 25 Create, edit and sign PDF forms & agreements According to this Table, Supplier A cannot provide more than 2,000 lb of oranges; if O.J. purchase 1,000 lb oranges from supplier A, after sorting (separating the oranges according to grade), O.J. can have 50 lb oranges of grade 3, 200 lb of grade 6, 500 lb of grade 8 and 250 lb of grade 10. Start Free Trial Week 7... A-06-20... LinAlg_... tut-probl... tps-05-2... test-pro... 37141Le... 37141Le... 37141-a... x @ Sign In Home A Tools CD @ Q 3.14 A n o 95.2% T de Share The purchased oranges are transported from suppliers to 0.J's warehouses. The transportation cost per lb is shown as an example in the Table below supplier1 supplier2 supplier3 Shipping cost($ per lb) Warehouse A Warehouse B Warehouse C 0.10 0.15 0.05 0.25 0.09 0.12 0.12 0.10 The sorting process takes place in 0.J's different warehouses at different cost rate. The amount of oranges sorted by each warehouse must be within its capacity. The sorted oranges are transported to OJ's plant to produce orange juice and bag of oranges. The average quality of oranges sold in bags must be at least 6, and the average quality of the oranges used to produce orange juice must be at least 7.5. The average quality is calculated as the weighted average of the grades of oranges blended together. For example, the average quality of blending 2 lb of grade 2 oranges and 5 lb of grade 9 oranges is 2 x 2 +9 x 5 2+5 The transportation cost from warehouse to plant is $0.05 per lb. Each lb of orange can yield 0.95 lb of bags of orange at a cost of $0.1, while each lb of orange can yield only 0.6 lb of orange juice at a cost of $0.4. The orange juice can be sold at $3.5 per lb, and the bag of oranges is sold at $1.5 a pound. O.J.'s plant can process no more than 30,000 lb of oranges, and must produce at least 3000 lb of bags of oranges. Oranges not used must be sent to a recycling centre at the cost of $0.1 per lb. 0.J. needs to find the optimal production and shipping plan to maximise profit. The detailed data can be found in the Excel file with the name 2020Assign- mentData.xlsx. Questions 1 Investigate how to solve 0.J.'s problem with Linear Programming 2 0.J. is considering to build a new plant. Discuss what data is required for assessing this strategic decision. ASSESSMENT TASKS: AutoSave OFF HE S U 2020AssignmentData Home Insert Draw Page Layout Formulas Data Review Share Comments Get Add-ins View Tell me h-Bv Nu Recommended vs Charts A Slicer Timeline A Av v TT Equation v IT Equation Pivot Recommended Table Table Pivot Tables Pictures Shapes Icons - My Add-ins Maps Pivot Chart Sparklines 5 Link New Comment Text Header & a Box Footer Symbol H I J K L M N O P Q Orange grade grade 7 (%) grade 4 (%) grade 5 (%) grade 6(%) grade 8(%) grade 9(%) grade 10(%) 5 0.3 G78 - XVfx Data for the assignment problem 2 Orange suppliers Purchase Supplier capacity(lb) Cost ($/b) grade 3 (%) 4000 5000 0.2 9000 6000 0.25 3000 0.15 5500 4500 0.18 12 5000 0.22 13 7000 0.25 3500 0.3 0.2 MIN 0.22 15 16 Transportation cost from supplier to warehouse ($/1b) warehouses 19 Supplier 20 22 23 5 0.14 0.06 0.14 0.09 0.09 0.11 0.15 0.11 0.13 0.1 0.15 0.1 0.12 0.1 0.07 0.12 0.05 0.05 0.09 0.11 0.13 0.1 0.05 0.06 0.15 0.1 0.14 0.12 0.13 29 0.13 31 Sorting at warehouses 32 33 warehouses 34 35 capacity (lb) 36 sorting cost ($/lb) 15000 0.12 20000 0.1 20000 0.11 37 38 Transporation cost from warehouses to plant ($/lb) 0.05 39 40 Processing at the plant 41 42 43 Average Quality Rate Products orange juice bag of orange + @ 0 - - + 100% AutoSave OFF HE S U 2020AssignmentData Home Insert Draw Page Layout Formulas Data Review Share Comments Get Add-ins View Tell me h-Bv Nu Recommended Charts the Slicer e A A Av TT Equation Pivot Recommended Table Table Pivot Tables Pictures Shapes Icons - My Add-ins Maps Pivot Chart Sparklines 5 Timeline Link New Comment Text Header & a Box Footer Symbol G78 X v fx L M N O P 10 11 5500 4500 5000 7000 3500 0.22 0.18 0.22 0.25 do BODO 12 13 14 0.3 16 Transportation cost from supplier to warehouse ($/1b) 17 warehouses 18 19 Supplier 20 0.1 0.15 0.14 0.06 0.14 0.09 0.09 0.11 0.15 0.11 0.13 0.13 0.12 0.1 0.07 0.12 0.05 0.05 0.09 0.11 0.13 0.1 0.05 0.06 0.15 0.1 0.14 0.12 0.13 31 Sorting at warehouses warehouses 33 34 35 36 capacity (lb) sorting cost ($/lb) 15000 0.12 20000 0.1 20000 0.11 37 0.05 42 38 Transporation cost from warehouses to plant ($/1b) 39 40 Processing at the plant 41 Products bag of orange orange juice 43 Average Quality 44 Yield 0.95 45 processing cost ($/1b) 0.1 46 selling price ($/lb) 47 minimum production 3000 0.6 1.5 0.4 3.5 49 processing capacity at the plant(lb) 30000 0.1 51 recycling cost (S/1b) 52 53 Rate + @ 0 - - - + 100%