What are the key relationships in the problem?

Dwarka's Reginal Planning The SOUTHERN CONFEDERATION OF DWARKA is a group of three Zamindars (communal farming communities) in India. 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 Zamindar 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 Table 1. Table 1: Resource data for the Southern Confederation of Dwarka 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 Confederation of Dwarka, as shown in Table 2. Table 2: Crop data for the Southern Confederation of Dwarka Because of the limited water available for irrigation, the Southern Confederation of Dwarka will not be able to use all its irrigable land for planting crops in the upcoming season. To ensure equity between the three Zamindars, it has been agreed that every zamindar will plant the same proportion of its available irrigable land. For example, if zamindar 1 plants 200 of its available 400 acres, then zamindar 2 must plant 300 of its 600 acres, while zamindar 3 plants 150 acres of its 300 acres. However, any combination of the crops may be grown at any of the lands. The job facing the Coordinating Technical Office is to plan how many acres to devote to each crop at the respective land while satisfying the given restrictions. The objective is to maximize the total net return to the Southern Confederation of Dwarka as a whole