I have an exam in a few hours. I need to understand the solution to the following question Find

desertiev5 2022-07-03 Answered
I have an exam in a few hours. I need to understand the solution to the following question

Find the Maximal to the the following 2 x 1 + 3 x 2 is the objective function.

The constraints are
4 x 1 + 3 x 2 600 ;
x 1 + x 2 160 ;
3 x 1 + 7 x 2 840 ;
x 1 , x 2 0.
Also the answer should be in the "Dual". If its possible please do it in the Algebraic method. If not I would just like the solution using the tableau method and how do you arrive to the solution.(PS: Any help would be great. )
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Answers (1)

Jenna Farmer
Answered 2022-07-04 Author has 17 answers
First of all, to solve this with the simplex method (tableau method) the inequalities of the contraints should be equalities. So you have to use slack variables.

4 x 1 + 3 x 2 600
x 1 + x 2 160
3 x 1 + 7 x 2 840
x 1 , x 2 0

4 x 1 + 3 x 2 + x 3 = 600
x 1 + x 2 + x 4 = 160

3 x 1 + 7 x 2 + x 5 = 840
x 1 , x 2 , x 3 , x 4 , x 5 0
Then can you continue by creating the tableau?

As regards the Algebraic method:

Draw the x 1 -axis and the x 2 -axis. Then from the first contraint you get:

4 x 1 + 3 x 2 600 :  when  x 1 = 0 x 2 = 200  and when  x 2 = 0 x 1 = 150. So you get the line as below, and since it is 600 the feasible region is below this line

Can you do this for the other contraints and find the solution? You should also keep in mind that x 1 , x 2 0
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