Possible title: Linear Optimization Problem: Finding Optimal Solutions

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    Linear Optimization
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Discussion Overview

The discussion revolves around a linear optimization problem where participants are attempting to maximize a function subject to several constraints. The focus is on verifying the correctness of proposed solutions and understanding the implications of the calculations involved.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a linear optimization problem and provides initial values for the variables, questioning their correctness.
  • Another participant suggests a correction regarding the formulation of the objective function, indicating a potential typo in the variable representation.
  • There is a discussion about the calculated value of the objective function, with one participant asserting that the value should be 54 based on the provided variable values.
  • Further clarification is sought regarding the calculation of the objective function, with participants discussing how to arrive at the value of 54.
  • A participant offers a link to check optimal solutions for linear programming problems, indicating a resource for further exploration.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the correctness of the initial values and the calculation of the objective function. There is no consensus on the final correctness of the proposed solutions, and multiple viewpoints regarding the calculations are present.

Contextual Notes

Participants have not fully resolved the discrepancies in the calculations and the potential typo in the objective function. The discussion reflects ongoing exploration of the problem without definitive conclusions.

goosey00
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Linear Optimization Problem follow up

Maximize: z=2x2+5x2+x3
x1+x2+x3 less then or equal to 12
x1-x2 less then or equal to 15
x2+2x3 less then or equal to 10
x1, x2 and x3 is greater then or equal to 0
x1= x2= x3= s1= s2= s3= z=
I get x1=2, x2=10 x3=0 s1=0 s2=0 s3=0 z=0
Is this wrong??
 
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Re: Linear Optimization Problem follow up

goosey00 said:
Maximize: z=2x2+5x2+x3 I assume that the first x2 should be x1.
x1+x2+x3 less then or equal to 12
x1-x2 less then or equal to 15
x2+2x3 less then or equal to 10
x1, x2 and x3 is greater then or equal to 0
x1= x2= x3= s1= s2= s3= z=
I get x1=2, x2=10 x3=0 s1=0 s2=0 s3=0 z=0
Is this wrong??
It looks as though $x_1=2,\ x_2=10,\ x_3=0$ is correct, but why do you get $z=0$? The condition $z=2x_1+5x_2+x_3$ says that $z$ should be 54 for those values of the $x$'s.
 
Re: Linear Optimization Problem follow up

Opalg said:
It looks as though $x_1=2,\ x_2=10,\ x_3=0$ is correct, but why do you get $z=0$? The condition $z=2x_1+5x_2+x_3$ says that $z$ should be 54 for those values of the $x$'s.

So where do you get 54?
BTW-you are right, it was suppose to be 1.
 
Re: Linear Optimization Problem follow up

goosey00 said:
So where do you get 54?
BTW-you are right, it was suppose to be 1.

If you plug in $x_1=2$, $x_2=10$ and $x_3=0$ into $z=2x_1+5x_2+x_3$ you get $z=(2 \times 2) + (5 \times 10) + 0=54$.
 
Re: Linear Optimization Problem follow up

goosey00 said:
Maximize: z=2x2+5x2+x3
x1+x2+x3 less then or equal to 12
x1-x2 less then or equal to 15
x2+2x3 less then or equal to 10
x1, x2 and x3 is greater then or equal to 0
x1= x2= x3= s1= s2= s3= z=
I get x1=2, x2=10 x3=0 s1=0 s2=0 s3=0 z=0
Is this wrong??

Hi goosey00, :)

You can check the optimal solutions of linear programming problems >>here<<.

Kind Regards,
Sudharaka.
 

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