A greenhouse farmer plans to grow three crops—cucumber, potato, and tomato—in the forthcoming 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:

Students may think that fertilizers contain NPK (nitrogen, phosphorus, potassium) and micronutrients 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.

Transcribed Image Text:

Revenue Yield Nitrogen Phosphorus Potassium Micronutrients £/kg (ton/ha) (kg/ha) (kg/ha) (kg/ha) (kg/ha) Cucumber 1.00 1.25 1.15 Total available nutrients Potato Tomato 300 110 240 475 209 500 2000 225 99 250 9100 700 300 600 24000 300 110 152 7500