I really do not know how to do this problem!! solve the given linear programming problem. Maximize z=2x+9y subject to x=0, y=0, x+y=10, x+2y=10 What is the solution The maximum value of z is z=_____, and it occurs at the point (x,y)=_____

Question

I really do not know how to do this problem!!
solve the given linear programming problem.
Maximize z=2x+9y subject to x>=0, y>=0, x+y<=10, 2x+y>=10, x+2y>=10
What is the solution
The maximum value of z is z=_____, and it occurs at the point (x,y)=_____

anonymous · Answer

@primeralph could you help me?

primeralph · Answer

know calculus?

primeralph · Answer

ever heard of Lagrange multipliers?

anonymous · Answer

no I haven't heard of it.

terenzreignz · Answer

Simplex algorithm?

primeralph · Answer

@terenzreignz  really? I don't think he/she has.

primeralph · Answer

@flutterflies  you can just do it by picking points

terenzreignz · Answer

Well, in lieu of Simplex, then since this is a linear program, just graph.

anonymous · Answer

Sorry I haven't. the prof doesn't use terms. and picking points??

terenzreignz · Answer

The optimal solution is always at a vertex of the feasible region...

terenzreignz · Answer

Anyway.... graphing linear inequalities is the name of the game here.

terenzreignz · Answer

Let's start with $\large x+y \le 10$

primeralph · Answer

yeah, just pick points that fall in and graph or generalize if you have the time

terenzreignz · Answer

Not just any points, but points at the corners... anyway, let's graph $\large x+y \le10$
It looks something like this...
|dw:1368765202264:dw|
Where the (tentative) feasible region is that triangle which you saw formed... (since x and y must both be positive)

terenzreignz · Answer

Now, superimpose the graph of $\large 2x+y \ge 10$

terenzreignz · Answer

|dw:1368765289662:dw|

terenzreignz · Answer

And now, our tentative feasible region is this...|dw:1368765378795:dw|
(sorry, the draw option has no "fill" tool)