i got a question like this:

Use the technique developed in this section to solve the minimization problem.

Minimize C=x-3y+z

subject to x-2y+3z<=30

2x+y-2z<=45

2x+y+3z<=40

x>=0, y>=0, z>=0

so i try to use simplex method to solve it, but...

1 -2 3 1 0 0 0 30

2 1 -2 0 1 0 0 45

2 1 3 0 0 1 0 60

-1 -3 -1 0 0 0 1 0

am i doing right to set up the initial simplex tableau?

i dont know what i should do with this: C=x-3y+zalso, what pivot element should i choose?

if the question like this:

2 1 3 1 0 0 45

4 1 5 0 1 0 45

-1 -2 -1 0 0 1 100

thank you so much