How do you graph a system of constraints, find all vertices, and evaluate the objective function at each vertex to find the maximum or minimum value.?

Question

anonymous · Answer

just like you described.  the constraints (if linear) can be easily graphed.  For each pair of lines, find the intersection (that will be a vertex). check the functional value at each vertex and compare to find the min or max.

anonymous · Answer

can youmshow me how like an example?

anonymous · Answer

do you want me to give you an equation?

anonymous · Answer

suppose you have 
$$y \ge3, x \le5, x+y=2$$
as constraint and 
$$f \left( x,y \right)=x+2y$$
as the function you want to maximize.

anonymous · Answer

sorry, let
$$y \le3, x \le5, x+y \le6$$
be your constraints

anonymous · Answer

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also, $$y \ge0, x \ge0.$$

anonymous · Answer

you only need to find the points of intersection and evaluate f(x,y) at those points and compare to find the max or min as required.

anonymous · Answer

this is the equation

anonymous · Answer

that kind of confused me a bit cause these equations are a little simpler

anonymous · Answer

so graph each as if it were = instead of $$\le \text{ or } \ge$$

anonymous · Answer

sorry.

anonymous · Answer

ok and its ok

anonymous · Answer

whats next?

anonymous · Answer

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