Linear Programming

[Kristen_Opp]

Maximize P=5x + 7y

subject to
2x+3y <(or=) 45
4x-21y>(or=) 6
x,y >(or ) 0

I don't know how to do this!?!?! Help...I have several problems like it and if someone could walk me through this one I could do the rest! THANK YOU

 

[morson]

Subject to all of those conditions?

 

[tkhunny]

With only two variables, there is an easy backup plan. Find all the corners and intesections and try them in your function to be maximized. You will find the right one.

 

[stapel]

The steps are pretty simple, once you have the constraints:

Solve the constraints for "y>" or "y<", and graph the inequalities. (Also graph the "x > 0" constraint.) For instance, the first constraint gives you "y < -(2/3)x + 15", and you would shade below the line.

Find the corners of the closed-off area that is formed by the inequalities. (That is, working with pairs of lines, "y=", find the intersection points of the lines.) For instance, y = -(2/3)x + 15 and y = 0 intersect at (x, y) = (45/2, 0).

Plug the corner points into the optimization equation. Whichever point gives you the biggest value for P is the solution point.

That's all there is to it!

Eliz.