Review set
Solving in Two Variables by Drawing
Plot the region, locate the direction of improvement, and push the objective until it leaves. Cases are chosen so the answer is not always a single corner: one has parallel contours giving a whole edge of optima, one recedes without limit, and one is empty.
What this involves
Retrieval after a delay, which is what makes knowledge durable.
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What this covers
- Solve a two-variable linear program graphically
Given a linear program in two variables, the learner can identify the feasible region from its constraints, determine which vertex or edge the objective contour last touches, compute the exact optimal solution by solving the tight constraints, and state whether the optimum is unique.
- Plot a linear inequality and identify its allowed side
Given one or more linear inequalities in two variables, the learner can draw each boundary line, determine which side the inequality allows by testing a point, and shade the set satisfying all of them together, including sign restrictions.
- Locate the direction of improvement for a linear objective
Given a linear objective and a direction of optimisation, the learner can draw or describe the contour family, identify the coefficient vector as the direction of increase, decide whether a proposed direction improves the objective, and state which way a contour must be pushed.