Lineaer Programming: How does x>= 1/4(x+y) simplify to?

3x%26gt;=Y or -3X+Y%26lt;=0. Also How would you graph this constraint?





Thanks.Lineaer Programming: How does x%26gt;= 1/4(x+y) simplify to?
x %26gt;= 1/4(x+y)





Multiply both sides by 4.


4x %26gt;= x + y


Subtract x from both sides.


3x %26gt;= y


or y %26lt;= 3x





How to graph:


The y-intercept is 0, so place a dot at y = 0.


The slope is 3 or 3/1, so from the point (0,0), move up 3 and to the right by 1. Place a dot there.


Connect the dots with a solid straight line.


Pick a test point (not on the line) to determine whether to shade above or below the line.


You will see that it is shaded below the line.