What does the region 3x + 2y at most 12 look like? Draw one inequality, then several together, and shade the points that satisfy them all. Learn to tell a bounded region from an unbounded one, and to find its corner points by solving pairs of boundary lines.
3 lessons, about 1 h 15 min3 simulations10 problems3 practice questionsPython in every lesson
Created by StemPy LabA linear inequality such as describes every point on one side of a line. To draw it, plot the boundary line first. Then test one point to see which side to shade. A solid line means the points on it are allowed, and a dashed line means they are not. The conditions and keep the picture in the first quadrant, where real quantities such as pens and hours live.
A point must obey every rule at once. The points that do form the feasible region, which you find by shading each inequality and keeping the overlap. The region can be closed in on all sides, which is bounded, or it can run on for ever, which is unbounded. When the rules contradict each other, no point is left. Then the problem has no feasible solution.
A corner point of the feasible region is a point where two boundary lines meet and which obeys every constraint. To find the corners, solve the equations of every pair of boundary lines, including the two axes. Then keep the solutions that pass all the inequalities. The corner points matter because, in the next course, the best plan always sits at one of them.
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