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

z=10

x1=0

x2=0

x3=3.33

Step-by-step 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