Paul is a farmer in Georgia and he is planning to grow rice, wheat, and cotton on his farm. He has 100 hectares of land and 120,000 m3 of irrigation water to use. Farmer Paul is planning to plant 30 hectares of rice, 40 hectares of wheat, and 30 hectares of cotton this year. The first table contains the fully irrigated water demand, the maxi- mum yield per hectare, and the expected profit per ton for these three crops. The ratios of actual-to-maximum yield for each of these three crops under different irrigation levels are shown in the second table. Help Farmer Paul find an optimal cropping pattern so that he can maximize his profit for this year.
Water Demand, Maximum Yield, and Profit by Crop
|
|
Water Demand (m3/ha)
|
Maximal Yield (tons/ha)
|
Profit ($/ton)
|
|
Rice
|
1,300
|
9
|
190
|
|
Wheat
|
1,200
|
12
|
180
|
|
Cotton
|
1,500
|
8
|
240
|
Maximum and Actual Yield by Irrigation Percentage by Crop
Maximum Yield Actual Yield by Irrigation Level Irrigation Level (tons/acre)
|
|
100%
|
80%
|
60%
|
|
100%
|
80%
|
60%
|
|
Rice
|
100%
|
92%
|
78%
|
|
9.00
|
8.28
|
7.02
|
|
Wheat
|
100%
|
88%
|
80%
|
|
12.00
|
10.56
|
9.60
|
|
Cotton
|
100%
|
72%
|
69%
|
|
8.00
|
5.76
|
5.52
|