New Age Math
posted by Meghan .
Suppose that y≤5x,3x≤y and 14x+15y≤1 together with 0≤x, 0≤y.
The maximum value of the function y+x on the resulting region occurs at x=? and y=?
The maximum value of the function is ?

Plot the lines on an x,y graph
y=5x and
y=14/15 x+1/15
x=0, y=0
Now you know any possible x,y will be inside or on the boundries of that region bounded by those four lines.
There is a nice theorem in Linear algebra, that says the maximum (or miniumum) of any objective function will be on the boundry lines,somewhere.
So do this: look at the coordinates where the lines intersect. Test your objective function Obj=x+y and see where it is maximum, you will quickly see out of those four intersections, you will find the maximum.
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