Graphing Systems of Linear Inequalities, in Depth
Read this topicProblems 5
- How many lattice points (points whose coordinates are both integers) satisfy the inequalities x+y≤11x+y \le 11x+y≤11, x≥1x\ge 1x≥1, and y≥1y \ge 1y≥1?
- Is there a system of linear inequalities ax+by+c≥0ax+by+c \ge 0ax+by+c≥0 (for real constants a,b,ca,b,ca,b,c) whose graph in the plane forms a concave quadrilateral?
- At most how many regions in the plane do 333 lines create? (Alternative formulation: Using only 333 vertical cuts, how many pieces can you slice a circular pie into?)
- At most how many regions in the plane do 444 lines create? (Alternative formulation: Using only 444 vertical cuts, how many pieces can you slice a circular pie into?)
- At most how many regions in the plane do 555 lines create? (Alternative formulation: Using only 555 vertical cuts, how many pieces can you slice a circular pie into?)