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71 : | ,. . / Q ) : ( 4 ) A family working in agriculture owns 125 acres of land and 40,000 dinars for investment. Family members can provide 3,500 hours of work during the winter months and 4,000 hours of work during the summer months. If the family has unused working hours, then young members of the family are directed to work on the neighbors' farm for 5 dinars an hour during the winter months and 6 dinars an hour during the summer months. Income cash the family gets from growing 3 types of crops, which are soybeans, corn and beetroot, and raising two types of animals, which are dairy cows and layer chickens. Cultivation of the three previous crops does not require invested sums, while raising each dairy cow needs an initial investment of about 1200 dinars, and raising each chicken needs 9 dinars, and each cow needs 1.5 acres of land, 100 working hours in the winter months and 50 working hours in The months of the summer season, while each cow produces an annual income of 1500 dinars. As for chickens, they do not need any part of the land, while one hen needs 0.6 work hours during the winter months and 0.3 hours of work during the summer months, while the productivity of one chicken is 3 dinars per year. The family's brix can accommodate a maximum of 3000 chickens, = hen needs 0.6 work hours during the winter months and 0.3 hours of work during the summer months, while the productivity of one chicken is 3 dinars per year. The family's brix can accommodate a maximum of 3000 chickens, while the available cowshed bar accommodates a maximum of 32 COWS. The following table shows the work hours required for each of the three types of agricultural crops per acres, as well as the income per acres of the three types: Beetroot Corn Soybean 10 35 20 Winter Work hours 40 75 50 Summer work hours 450 900 600 Net annual income (in dinars per acre) The family wants to know the area of land that should be planted with each of the three types of agricultural crops, as well as the number of cows and chickens that must be owned, and the number of overtime hours on the neighboring farm in order to achieve the maximum possible profit for the family Required: To formulate a linear programming model that expresses the given .problem Note: Formulate a target function for this issue plus 4 Restrictions (at least) .that address this issue : 60 ) Convert the following linear programming model from legal to standard form Min Z = 2 X1 + X2 30 s s.t: X1 +3 X2 40 s 4 X1 + 2 X2 Os X1, X2 : 55 3/1 71 : | ,. . / Q ) : ( 4 ) A family working in agriculture owns 125 acres of land and 40,000 dinars for investment. Family members can provide 3,500 hours of work during the winter months and 4,000 hours of work during the summer months. If the family has unused working hours, then young members of the family are directed to work on the neighbors' farm for 5 dinars an hour during the winter months and 6 dinars an hour during the summer months. Income cash the family gets from growing 3 types of crops, which are soybeans, corn and beetroot, and raising two types of animals, which are dairy cows and layer chickens. Cultivation of the three previous crops does not require invested sums, while raising each dairy cow needs an initial investment of about 1200 dinars, and raising each chicken needs 9 dinars, and each cow needs 1.5 acres of land, 100 working hours in the winter months and 50 working hours in The months of the summer season, while each cow produces an annual income of 1500 dinars. As for chickens, they do not need any part of the land, while one hen needs 0.6 work hours during the winter months and 0.3 hours of work during the summer months, while the productivity of one chicken is 3 dinars per year. The family's brix can accommodate a maximum of 3000 chickens, = hen needs 0.6 work hours during the winter months and 0.3 hours of work during the summer months, while the productivity of one chicken is 3 dinars per year. The family's brix can accommodate a maximum of 3000 chickens, while the available cowshed bar accommodates a maximum of 32 COWS. The following table shows the work hours required for each of the three types of agricultural crops per acres, as well as the income per acres of the three types: Beetroot Corn Soybean 10 35 20 Winter Work hours 40 75 50 Summer work hours 450 900 600 Net annual income (in dinars per acre) The family wants to know the area of land that should be planted with each of the three types of agricultural crops, as well as the number of cows and chickens that must be owned, and the number of overtime hours on the neighboring farm in order to achieve the maximum possible profit for the family Required: To formulate a linear programming model that expresses the given .problem Note: Formulate a target function for this issue plus 4 Restrictions (at least) .that address this issue : 60 ) Convert the following linear programming model from legal to standard form Min Z = 2 X1 + X2 30 s s.t: X1 +3 X2 40 s 4 X1 + 2 X2 Os X1, X2 : 55 3/1