Question

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 ?

Answer 1

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.