I'm learning the simplex method and solved some exercises but I'm having trouble solving simple exercises that already comes in standard form, example:

min z = 8x1 + 2x2 + 7x3

subject to:

2x1 + 2x2 + x3 = 5

x1 , x2 , x3 ≥ 0

The linear program is already in standart form.No need to add slack variables so how to solve the exercise with simplex algorithm?

On what basis I start the simplex?

The same problem occurs in the exercise below.

min z = x1 − 3x2 + 3x3

subject to:

x1 − 3x2 + 2x3 = 0

x1 + x2 + x3 = 1

x1 , x2 , x3 ≥ 0

Thanks