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please use lingo and explain in details, thank you. 5. Three prairie farmers, Boyarchuk, Jorgensen, and Paisley, have decided to form a co-operative for the
please use lingo and explain in details, thank you.
5. Three prairie farmers, Boyarchuk, Jorgensen, and Paisley, have decided to form a co-operative for the crop growing aspect of their farming business so that they can share resources such as expensive harvesting equipment, limited water supplies for irrigation, etc. The table below shows the amount of arable land each farmer owns and the amount of water allocated by a provincial water authority to each farmer for irrigation. The farmers have considered several crops that are suited for the region and have decided to grow the following three crops: maize, corn, and wheat. These crops yield different expected net profits per hectare and consume different amounts of water. In addition, provincial agricultural recommendations set maximum quotas for the total area that can be devoted to each of these crops by the farmers' co-operative. The relevant information is shown in the table below. The agreement worked out between Boyarchuk, Jorgensen, and Paisley stipulates that each farmer will use at least 60% of his available land for planting crops. The remaining 40% may be used for other farm activities such as grazing cattle and sheep, but this lies outside the farmers' agreement. Also, to meet local demand they have agreed that at least 10 hectares of wheat must be planted in total, and each one should plant at least 3 hectares. In addition, to ensure the faimess, each individual profit should be no less than 25% of the total profit. (a) Formulate a linear program to maximize the total profit of the three farmers. The decision variables can be defined a the number or acres of each type of crop to be planted by each farmer. The following table shows the decision variables for each crop-farmer combination. (For example, MB refers to the number of hectares of maize planted by Boyarchuk.) (b) Solve the model using LINGO. (c) Specify the number of hectares of each crop should be planted and the percentage of net profit does each farmer obtain Step by Step Solution
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