A farmer with 1200 acres is considering planting three different crops, corn, soybeans, and oats. The farmer wants to use all 1200 acres. Seed corn costs $20 per acre, while soybean and oat seed cost $50 and $12 per acre respectively. The farmer has $40 000 available to buy seed and intends to spend it all.
(a) Use the information above to formulate two linear equations with three unknowns and solve it.
(b) Solutions to the system are choices that the farmer can make. Write down two reasonable solutions.
(c) Suppose that in the fall when the crops mature, the farmer can bring in revenue of $100 per acre for corn, $300 per acre for soybeans and $80 per acre for oats. Which of your two solutions in the prior part would have resulted in a larger revenue?