A local farmer knows that he is able to sell his oats for $500.00 per acre and his corn for $450.00 per acre. He has a total of 150 hours to work in the fields. He has 70 acres available to plant. He calculates that it will take 3 hours of labour per acre of oats and 2 hours of labour per acre of corn to plant and care for the crops.

Question

A local farmer knows that he is able to sell his oats for $500.00 per acre and his corn for $450.00 per acre.  He has a total of 150 hours to work in the fields.  He has 70 acres available to plant. He calculates that it will take 3 hours of labour per acre of oats and 2 hours of labour per acre of corn to plant and care for the crops.

Sketch the feasible region.

GPT 3.5 · Answer

To sketch the feasible region, we need to represent the constraints given in the problem.
Let's first define our variables:
Let x be the number of acres of oats.
Let y be the number of acres of corn.

Now, let's consider the constraints:
1) The farmer has a total of 150 hours to work in the fields.
We can represent this constraint as:
3x + 2y ≤ 150

2) The farmer has 70 acres available to plant.
We can represent this constraint as:
x + y ≤ 70

3) Non-negativity constraint:
x ≥ 0 and y ≥ 0

Now, let's plot these constraints on a graph:
Graph: https://www.desmos.com/calculator/qatlr3asx2

The feasible region is the shaded region that satisfies all the constraints: