Solving a linear programme on a graph
Solving a two-variable programme on the plane: line and half-plane of each constraint, feasible region, isoprofit lines, optimal vertex, the vertex method and the four possible outcomes.
- 28 cards
- 6 topics
- Free
The outline, topic by topic
Each topic is weighted the way the exam weighs it.
- Concepts
- Questions
- Sort and link
- The numbers
- The curves
- The steps
A few cards from the deck
Graphical method: what is it?
Show the answer
Solving a two-variable programme by drawing its constraints in the plane and finding on the drawing the point that gives the best value.
It works only with two variables (a plane). Beyond that, an algebraic method such as the simplex is used.
The constraint x + y ≤ 80 is drawn. Which half-plane do we keep, with x ≥ 0 and y ≥ 0?
- The origin's side, below the line
- The one not containing the origin, lying above
- Both, since the line separates them
- Only the points on the line
Show the answer
The origin's side, below the line
0 + 0 ≤ 80 is true: the origin meets the constraint. Points on the line belong to it (≤ is non-strict) but are not the only ones: the whole half-plane below is feasible too.
When the maximum exists and the region has vertices, it is reached at at least one … of the feasible region.
Show the answer
When the maximum exists and the region has vertices, it is reached at at least one vertex of the feasible region.
The objective has degree 1: sliding the isoprofit line, the last contact with a polygon happens at a corner (or along a side whose two ends are corners).