12. A greenhouse farmer plans to grow three crops cucumber, potato, and tomato-in the forth- coming...

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12. A greenhouse farmer plans to grow three crops cucumber, potato, and tomato-in the forth- coming season in his farm, which spans 60 hectares. Each crop requires nitrogen, phosphoros, potassium, and micronutrients. The resource requirement for each crop and the total resources available are as follows: Revenue Yield Nitrogen /kg (ton/ha) (kg/ha) Phosphorus (kg/ha) (kg/ha) Potassium Micronutrients (kg/ha) Cucumber 1.00 300 475 225 700 300 Potato 1.25 110 209 99 300 110 Tomato 1.15 240 500 250 600 152 Total available nutrients 2000 9100 24000 7500 Students may think that fertilizers contain NPK (nitrogen, phosphorus, potassium) and micronutri- ents in a certain ratio and can't be separated. Nowadays, companies sell theses nutrients separately. Given the resource and land constraints, the farmer wants to know how many hectares of each type of crop to plant in the season to maximize revenue. a. Formulate a linear programming model. b. Solve the model by using the computer. 12. A greenhouse farmer plans to grow three crops cucumber, potato, and tomato-in the forth- coming season in his farm, which spans 60 hectares. Each crop requires nitrogen, phosphoros, potassium, and micronutrients. The resource requirement for each crop and the total resources available are as follows: Revenue Yield Nitrogen /kg (ton/ha) (kg/ha) Phosphorus (kg/ha) (kg/ha) Potassium Micronutrients (kg/ha) Cucumber 1.00 300 475 225 700 300 Potato 1.25 110 209 99 300 110 Tomato 1.15 240 500 250 600 152 Total available nutrients 2000 9100 24000 7500 Students may think that fertilizers contain NPK (nitrogen, phosphorus, potassium) and micronutri- ents in a certain ratio and can't be separated. Nowadays, companies sell theses nutrients separately. Given the resource and land constraints, the farmer wants to know how many hectares of each type of crop to plant in the season to maximize revenue. a. Formulate a linear programming model. b. Solve the model by using the computer.