Help with Finite Math: Max z with Slack/Surplus Vars

[mike43414]

Add slack variables or subtract surplus variables, and set up the initial simplex tableau:

Maximize z = 5x₁ + 3x₂
subject to:
2x₁ + 5x₂ ≤ 50
x₁ + 3x₂ ≤ 25
4x₁ + x₂ ≤ 18
x₁ + x₂ ≤ 12
with x₁≥0, x₂ ≥ 0

Please help.

 

[HallsofIvy]

Why isn't this in the homework section? And why are you simply stating the problem without showing any work at all? Surely, if you are expected to be able to do a problem like this you must know something about it! What are "slack" variables? How many would you expect this problem to have? What is the "simplex tableau"?

Are you required to use the simplex tableau? Since there are only two variables, graphing the feasible region is the simplest thing to do.

 

[mike43414]

Sorry, I didn't realize that there was a homework help section. And it's not my homework, it's my cousin's. She's been in the hospital for the past week and half so she missed quite a few lectures and is having trouble with her homework. I have a degree in mechanical engineering, so everyone in my family assumes that I know almost everything about math (so not true). Well, I'm fairly certain that I've never done a problem like this before (or I just don't remember doing such problems), so I was looking anywhere for help. I read the chapter, and I got some idea of what the answer should be, but I'm just not sure. The chapter is on other ways to solve these kind of problems besides graphing.

We think that the answer to the first part is:
z=5x_1+3x_2
2x_1 + 5x_2 + s_1=50
x_1+3x_2 + s_2=25
4x_1+ x_2+s_3=18
x_1+ x_2 +s_4=12
x_1≥0, x_2≥0, s_1≥0, s_2≥0, s_3≥0, s_4≥0

(_1, _2, etc are subscripts)

And the tableau:
2 5 1 0 0 0 0 50
1 3 0 1 0 0 0 25
4 1 0 0 1 0 0 18
1 1 0 0 0 1 0 12
-5 -3 0 0 0 0 1 0


We're not sure if this is correct since a friend of hers said that she got something different.

 

[Mark44]

It looks like you are on the right track, or close to it. Here's a link to a tutorial that might help you out - http://people.hofstra.edu/Stefan_Waner/RealWorld/tutorialsf4/frames4_3.html

With a degree in ME, you might not have had a class in what is called Linear Programming, which includes solving problems like this one using the Simplex Algorithm.