Solutions of the given linear programming problem

[mathmari]

Hello!
Given the following linear programming problem
$$\min(2x + 3y + 6z + 4w)$$
$$x+2y+3z+w \geq 5$$
$$x+y+2z+3w \geq 3$$
$$x,y,z,w \geq 0$$
I am asked to find all the solutions using the simplex method.

To solve this problem we use the Two-Phase method, don't we?
Then I found that there are infinite many solutions, $(x,y,z,w)=(1-m, 2+0.4m, 0, 0.2m), 0≤m≤1$ with $min=8$.
Could you tell me if this is right?

 

[Opalg]

Hello!
Given the following linear programming problem
$$\min(2x + 3y + 6z + 4w)$$
$$x+2y+3z+w \geq 5$$
$$x+y+2z+3w \geq 3$$
$$x,y,z,w \geq 0$$
I am asked to find all the solutions using the simplex method.

To solve this problem we use the Two-Phase method, don't we?
Then I found that there are infinite many solutions, $(x,y,z,w)=(1-m, 2+0.4m, 0, 0.2m), 0≤m≤1$ with $min=8$.
Could you tell me if this is right?

Your answer is certainly correct, because if you add the two inequalities you get $2x + 3y + 5z + 4w \geqslant 5+3=8$. Therefore $2x + 3y + 6z + 4w \geqslant 8+z$, which is minimised by taking $z=0$. Your solutions, with $z=0$, clearly satisfy all the given conditions, so they must be right.

 

[I like Serena]

Hello!
Given the following linear programming problem
$$\min(2x + 3y + 6z + 4w)$$
$$x+2y+3z+w \geq 5$$
$$x+y+2z+3w \geq 3$$
$$x,y,z,w \geq 0$$
I am asked to find all the solutions using the simplex method.

To solve this problem we use the Two-Phase method, don't we?
Then I found that there are infinite many solutions, $(x,y,z,w)=(1-m, 2+0.4m, 0, 0.2m), 0≤m≤1$ with $min=8$.
Could you tell me if this is right?

Looks good! ;)

EDIT: Aargh, overtaken by Opalg.

 

[mathmari]

Your answer is certainly correct, because if you add the two inequalities you get $2x + 3y + 5z + 4w \geqslant 5+3=8$. Therefore $2x + 3y + 6z + 4w \geqslant 8+z$, which is minimised by taking $z=0$. Your solutions, with $z=0$, clearly satisfy all the given conditions, so they must be right.

Great! Thank you for your answer!

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Looks good! ;)

EDIT: Aargh, overtaken by Opalg.

Nice! Thank you!

 

[CellCoree]

Hello! It seems like you have correctly applied the Two-Phase method to solve the given linear programming problem. The result you have obtained is a set of feasible solutions with a minimum value of 8. However, it is important to note that there may be other feasible solutions that can also achieve this minimum value. To ensure that your solution is optimal, you can use the Simplex method to check for any alternative solutions that may have a lower objective function value. Overall, your approach and solution seem to be correct. Great job!