Farmer Richard owns 100 acres of rich farmland and must plan his year (January – December) to earn the most profit. Due to last year’s rains and floods he must overcome the losses with optimal planning and great yield. He has 4 different crops to pick from, but the timing of planting and harvesting each one is key to his success.
The Crops and Their Schedules
Corn
- Earnings per acre: $800
- Planting time: March
- Harvesting time: September
- Farm space used for: 6 months (March through September)
Tomatoes
- Earnings per acre: $1,200
- Planting time: May
- Harvesting time: August
- Farm space used for: 4 months (May through August)
Carrots
- Earnings per acre: $600
- Planting time: Choose either April or September
- Harvesting time: Pick between July or December
- Field usage period: Each cycle lasts 3 months
Soybeans
- Earnings per acre: $500
- Planting time: April
- Harvesting time: October
- Field usage period: 6 months (April through October)
Wheat
- Earnings per acre: $700
- Planting time: February
- Harvesting time: August
- Field usage period: 6 months (February through August)
Main Constraints and Timing Dependencies
IMPORTANT LIMITATION: Richard is restricted to planting ONE kind of crop across his entire 100-acre farm at a time. He isn’t able to divide his land to raise multiple crops at once.
- One Crop at a Time: The farmer has to use all 100 acres for the same crop during a planting season.
- Changing Crop Options: After finishing one harvest, Farmer Richard is allowed to switch to planting a different crop in the following season if time permits.
- Timing of Planting: Crops come with specific months when planting is possible, and those timelines cannot be adjusted.
- Waiting Period Rule: At least one month needs to pass between harvesting a crop and starting to plant a new one on the same field.
What You Need to Do
Figure out how Richard can use all 100 acres throughout the year to earn the most annual profit. Which crop sequence brings in the maximum yearly earnings?
——— View the answer ———–
Optimal Crop Schedule:
Plant tomatoes from May through August: 100 acres × $1,200 per acre = $120,000.
Grow carrots in fall, from September to December: 100 acres × $600 per acre = $60,000.
Grand Total: $180,000.
