explicitvogue one year ago Fan + Medal to best answer! Find the values of x and y that maximize the objective function P=3x+y for the graph. What is the maximum value? A. (0,6) B. (1,4) C. (3,0) D. (0,0) (Graph attached in replies)

1. explicitvogue

2. ybarrap

Here is a similar problem I solved about a year ago - http://openstudy.com/study#/updates/526d6f5ee4b0116e636910d2 Let me know if you need more help

3. ybarrap

Another approach is to use the method of Lagrange Multipliers -- do you know that?

4. ybarrap

Basically, the easiest approach is to just plug in each of those coordinates into P and see which makes it the largest. For example, the using the first coordinate $$P(0,6)=3\times 0 + 6=6$$ Now you do P(1,4). What does that equal?

5. explicitvogue

P(1,4)=3*1+4= 7?

6. ybarrap

yes, keep going like that - now find P(3,0)

7. explicitvogue

P=3*3+0=9 So the answer would be C?

8. ybarrap

Yes, because that made P the largest!

9. explicitvogue

I have never actually understood how to solve those problems, but the way you explained it seems so much easier than the way I learned it. Thank you so much!

10. ybarrap

The problem you have is if you did not have choices, you'll need to check the each point in the choices are in the domain given. For example, is (3,0) in the triangle you provided? It is, so this is a valid solution. How were you taught to maximize a function? Is this a calculus course?

11. explicitvogue

Oh, okay that makes sense. And I'm not exactly sure how to explain the way I learned it, but it seemed much more difficult. This is from an AP Algebra 2 course.

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