(1) Bundaberg sources ginger from three different farms and produces ginger beer at five different produc-...

 

Transcribed Image Text:

(1) Bundaberg sources ginger from three different farms and produces ginger beer at five different produc- tion plants. The production plan for the next month, i.e. July, requires (based on various capacity constraints) that a certain volume of ginger be processed at each of the different production plants. The volume (in cubic metres, m) of ginger to be processed at each of the five plants in July is shown in the following table: Plant 1 2 3 4 5 Ginger harvested this month (i.e. during June) is used for production in July. In June, the total harvest volume (in cubic metres, m) at each of the three farms is shown in the following table: Farm Volume (m) 9500 11 500 10 000 11 500 14 000 Farm A B C Volume (m) 17.500 18000 21000 The distances (in kilometres) between the respective farms and production plants are presented in the following table: Plant 3 1 2 4 5 362 451 193 367 A 269 B 560 232 290 395 624 C 323 536 250 419 601 Bundaberg employs different transportation service providers and, as a result, different transportation fleets at the three farms due to regional restrictions -Farm A employs Scania trucks, Farm B employs Volvo trucks, and Farm C employs Hino trucks. Consequently, a different fuel economy (expressed in terms of litres of fuel consumed per kilometre travelled) is applicable to each of the different trans- portation fleets. The price of fuel is expected to remain fixed at R17.50 per litre during the entire month of July. The fuel economy corresponding to the transportation fleets at the different farms is presented in the following table: Farm Fuel economy (l/km) A B C 0.250 0.275 0.240 The management of Bundaberg is tasked with ensuring that sufficient harvest volumes are transported from the ginger farms to the production plants in order to ensure that the production plan is strictly adhered to. The management of Bundaberg is seeking to minimise transportation cost. Formulate the problem mathematically as a balanced transportation problem. Define your decision variables precisely and include short explanatory comments for each model constraint. Show all your calculations. Fur- thermore, find the optimal solution(s) to this transportation problem using an appropriate computer implementation (e.g. Microsoft Excel's Solver add-on or Python packages such as SciPy & PuLP). In- terpret in words the solution obtained. Please include a carefully commented print-out of your program embedded within your PDF submission. [35] (1) Bundaberg sources ginger from three different farms and produces ginger beer at five different produc- tion plants. The production plan for the next month, i.e. July, requires (based on various capacity constraints) that a certain volume of ginger be processed at each of the different production plants. The volume (in cubic metres, m) of ginger to be processed at each of the five plants in July is shown in the following table: Plant 1 2 3 4 5 Ginger harvested this month (i.e. during June) is used for production in July. In June, the total harvest volume (in cubic metres, m) at each of the three farms is shown in the following table: Farm Volume (m) 9500 11 500 10 000 11 500 14 000 Farm A B C Volume (m) 17.500 18000 21000 The distances (in kilometres) between the respective farms and production plants are presented in the following table: Plant 3 1 2 4 5 362 451 193 367 A 269 B 560 232 290 395 624 C 323 536 250 419 601 Bundaberg employs different transportation service providers and, as a result, different transportation fleets at the three farms due to regional restrictions -Farm A employs Scania trucks, Farm B employs Volvo trucks, and Farm C employs Hino trucks. Consequently, a different fuel economy (expressed in terms of litres of fuel consumed per kilometre travelled) is applicable to each of the different trans- portation fleets. The price of fuel is expected to remain fixed at R17.50 per litre during the entire month of July. The fuel economy corresponding to the transportation fleets at the different farms is presented in the following table: Farm Fuel economy (l/km) A B C 0.250 0.275 0.240 The management of Bundaberg is tasked with ensuring that sufficient harvest volumes are transported from the ginger farms to the production plants in order to ensure that the production plan is strictly adhered to. The management of Bundaberg is seeking to minimise transportation cost. Formulate the problem mathematically as a balanced transportation problem. Define your decision variables precisely and include short explanatory comments for each model constraint. Show all your calculations. Fur- thermore, find the optimal solution(s) to this transportation problem using an appropriate computer implementation (e.g. Microsoft Excel's Solver add-on or Python packages such as SciPy & PuLP). In- terpret in words the solution obtained. Please include a carefully commented print-out of your program embedded within your PDF submission. [35]

Answer rating: 100% (QA)

To formulate the problem mathematically as a balanced transportation problem lets define the decision variables and constraints Decision Variables Let ... View the full answer