In Southern Region there are a group of three Zones (communal farming communities). Overall planning for...

  

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In Southern Region there are a group of three Zones (communal farming communities). Overall planning for this group is done in its Coordinating Technical Office. This office currently is planning agricultural production for the coming year. The agricultural output of each zone is limited by both the amount of available irrigable land and the quantity of water allocated for irrigation by the Water Commissioner (a national government official). These data are given in the following table. TABLE 1 Resource data for the Southern Confederation of the Three Zones Zable Land (Acer Allocation (An Fot 400 00 b 100 The crops suited for this region include sugar beets, cotton, and sorghum, and these are the three being considered for the upcoming season. These crops differ primarily in their expected net return per acre and their consumption of water. In addition, the Ministry of Agriculture has set a maximum quota for the total acreage that can be devoted to each of these crops by the Southern Region of Three Zones, as shown in Table 2 below. 500 500 375 TABLE 2. Crop data for the Southern region of Three Zones Crop Maximum Water Not Ratu Crop Quote Consumption Aures) A Sugar beet00 Sorghum 125 Because of the limited water available for irrigation, the Southern region of three zones will not be able to use all its irrigable land for planting crops in the upcoming season. To ensure equity between the three zones, it has been agreed that every zone will plant the same proportion of its available irrigable land. For example, if zone 1 plants 200 of its available 400 acres, then zone 2 must plant 300 of its 600 acres, while zone 3 plants 150 acres of its 300 acres. However, any combination of the crops may be grown at any of the zones. The job facing the Coordinating Technical Office is to plan how many acres to devote to each crop at the respective zone while satisfying the given restrictions. The objective is to maximize the total net return to the Southern region of three zones as a whole. 1. Formulate the problem as LP 2 Solve the problem using excel * Determine Range of feasibility and Range of optimality. In Southern Region there are a group of three Zones (communal farming communities). Overall planning for this group is done in its Coordinating Technical Office. This office currently is planning agricultural production for the coming year. The agricultural output of each zone is limited by both the amount of available irrigable land and the quantity of water allocated for irrigation by the Water Commissioner (a national government official). These data are given in the following table. TABLE 1 Resource data for the Southern Confederation of the Three Zones Zable Land (Acer Allocation (An Fot 400 00 b 100 The crops suited for this region include sugar beets, cotton, and sorghum, and these are the three being considered for the upcoming season. These crops differ primarily in their expected net return per acre and their consumption of water. In addition, the Ministry of Agriculture has set a maximum quota for the total acreage that can be devoted to each of these crops by the Southern Region of Three Zones, as shown in Table 2 below. 500 500 375 TABLE 2. Crop data for the Southern region of Three Zones Crop Maximum Water Not Ratu Crop Quote Consumption Aures) A Sugar beet00 Sorghum 125 Because of the limited water available for irrigation, the Southern region of three zones will not be able to use all its irrigable land for planting crops in the upcoming season. To ensure equity between the three zones, it has been agreed that every zone will plant the same proportion of its available irrigable land. For example, if zone 1 plants 200 of its available 400 acres, then zone 2 must plant 300 of its 600 acres, while zone 3 plants 150 acres of its 300 acres. However, any combination of the crops may be grown at any of the zones. The job facing the Coordinating Technical Office is to plan how many acres to devote to each crop at the respective zone while satisfying the given restrictions. The objective is to maximize the total net return to the Southern region of three zones as a whole. 1. Formulate the problem as LP 2 Solve the problem using excel * Determine Range of feasibility and Range of optimality.

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Crop 1 2 3 Sugar Beets x1 x2 x3 Cotton ... View the full answer