This is the initial tableau of a linear programming problem. Solve by the simplex method.

Step-by-step explanation:

We start by selecting our pivot column as the most negative value on the bottom row.

This means our pivot column is . We now generate a new column by diving our pivot value by our value on the right-most column. This gives us (on a new row)

P/V

12/1 = 12

4/2 = 2

4/1 = 4

We pick our smallest positive value to be our pivot row.

This means our pivot row is our second row, and our pivot column is our first column. We now divide our entire row by our pivot point (our intersection of these two pivots)

This gives us our new second row as

1 3 0 1/2 0 0 2

now we need to eliminate our values from our other rows.

old row 1 - new row 2 gives us new row 1

row two stays the same

old row 3 - new row 2 gives us new now 3.

old row P + 2 new row 2 gives us new row P  

After the first iteration of this algorithm this gives our tableau as: (see attached screenshot)