Systems of Linear Inequalities with 3 or More Variables
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- Consider the following system of linear inequalities: x+2y≤3x + 2y \le 3x+2y≤3 y+z≥5y + z \ge 5y+z≥5 2x−z≥42x - z \ge 42x−z≥4 What is the minimum value of xxx?
- Lynnelle took 101010 tests in her math class at Stanford. Her score on each test was an integer from 000 through 100100100. She noticed that, for every four consecutive tests, h…
- How many of the 8 octants does the plane x+y+z=0x+y+z = 0x+y+z=0 intersect? Note: There are 8 octants in space: for instance, one of them is x>0x>0x>0, y>0y>0y>0, z>0z>0z>0, whi…
- How many of the 8 octants in space contain points (x,y,z)(x,y,z)(x,y,z) such that x+y+z≥0.1x+y+z \ge 0.1x+y+z≥0.1? Note: There are 8 octants in space: for instance, one of them …
- Are there real numbers x,y,zx,y,zx,y,z such that x−y,y−z,z−xx - y, y-z, z-xx−y,y−z,z−x are all positive?
- Are there real numbers x,y,zx,y,zx,y,z such that x−2y,y−2z,z−2xx - 2y, y-2z, z-2xx−2y,y−2z,z−2x are all positive?
- If Phil used his time and energy as efficiently as possible, how many Good Things could he do in a given day of the loop?