Locating the Optimal Point
The objective line method
- For the objective line method, you draw a line for the equation to maximise. We only care about the gradient, not the y-intercept.
- We put our ruler on the line with this gradient, and we "fly" our ruler in towards the region, keeping the gradient the same.
- When our ruler hits a point on the region, then this point is the optimal point.
Example problem
- For \(x, y \geq0\)
- \(3x+y\leq15\)
- \(2x+5y\leq 20\)
- Maximise:
a) \(x+y\)
b) \(x+4y\)
Another example problem
1.