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

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In summary: However, if you are comfortable with calculus, you could still try to solve the problem yourself. The Simplex Algorithm is a mathematical technique used to solve problems that have two or more variables. It is a relatively simple algorithm, but it can be time-consuming to solve a large problem using it. In summary, the problem asks for the maximum value of z, which is 5x_1+3x_2, when subject to the constraints that x_1+x_2 must be less than or equal to 50 and x_1+x_2 must be less than or equal to 25. Since both x_1 and x_2 are greater than 0, the problem has two feasible solutions, each of which has a
  • #1
mike43414
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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.
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
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Related to Help with Finite Math: Max z with Slack/Surplus Vars

1. What is Finite Math?

Finite Math is a branch of mathematics that deals with the study of finite or discrete systems. It involves the application of mathematical principles to solve real-world problems in areas such as business, economics, and the social sciences.

2. What is Max z with Slack/Surplus Vars?

Max z with Slack/Surplus Vars refers to a method used in linear programming to find the maximum value of an objective function while considering the constraints of a system. It involves introducing slack and surplus variables to represent unused resources and excess resources, respectively.

3. How is Max z with Slack/Surplus Vars different from other optimization methods?

Max z with Slack/Surplus Vars is different from other optimization methods, such as the simplex method or the graphical method, because it takes into account the unused and excess resources in a system. This allows for a more accurate and efficient solution to be found.

4. What are some real-world applications of Max z with Slack/Surplus Vars?

Max z with Slack/Surplus Vars has various real-world applications, such as optimizing production processes in industries, maximizing profits in businesses, and allocating resources in government agencies. It can also be used in scheduling and planning problems, such as assigning tasks to workers or scheduling airline flights.

5. Are there any limitations to using Max z with Slack/Surplus Vars?

Like any mathematical method, Max z with Slack/Surplus Vars has its limitations. It is only applicable to linear systems and assumes that the relationships between variables are linear. It also requires the objective function and constraints to be known and well-defined, which may not always be the case in real-world problems.

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