Question

Find all optimal solutions to the following LP using the Simplex Algorithm:

maxz = x1 + 2x2 + 3x3
s.t.
x1 + 2x2 + 3x3 ≤ 10

x1 + x2 ≤ 5

x1 ≤ 1

x1,x2,x3 ≥ 0

Answer 1

z=10

x1=0

x2=0

x3=3.33

Explanation:

Answer 2

z=10

x1=0

x2=0

x3=3.33

Explanation:

First Step convert your constraints in standard equations

so we have

x1 + 2x2 + 3x3+x4 = 10

x1 + x2 +x5= 5

x1 +x6= 1

Now we pass it all to the simplex table

Remember that we choose the column with the most negative value

Pivot Element=3

Divide all elements on Pivot Line by Pivot Element

Line x5= 0*Pivot Line +Line x5

Line x6= 0*Pivot Line+ Line X6

Line Z= 3* Pivot Line + Line Z

We finish when all the elements from the line Z are positive

Hence we have that x3=3.33 and x1=0, x2=0 and the max of z is 10