Farm O.R.

By John Toczek

As a farmer, the decisions you make when planting crops influence whether your year will end with significant profits or in bankruptcy. As the owner of 1,000 acres, you need to make the following decisions for your upcoming planting season:

  1. Plant corn or soybeans
  2. Buy crop insurance
  3. Use fertilizer    

Corn has a profit of $190 per acre, but you will lose $190 per acre if your crop fails. Corn fertilizer costs $30,000 and corn insurance costs $35,000. Soybeans have a profit of $170 per acre, but you will lose $170 per acre if your crop fails. Soybean fertilizer costs $10,000 and soybean insurance costs $20,000.

Table 1 shows the probability of reaping a full harvest for either crop. For simplicity, assume that you will either successfully reap all 1,000 acres or there will be a total crop failure.

Farmers face a tough decision


What is your expected profit when the best decisions are made?

Send your answer to puzzlor@gmail.com by Dec. 15. The winner, chosen randomly from correct answers, will receive an “Analytics - Driving Better Business Decisions” T-shirt. Past questions can be found at puzzlor.com.

John Toczek is the manager of Decision Support and Analytics for ARAMARK Corporation in the Global Risk Management group. He earned a bachelor’s degree in chemical engineering at Drexel University (1996) and a master’s degree in operations research from Virginia Commonwealth University (2005).