Question: use the simplex method to find the maximum value of...

Use the simplex method to find the maximum value of P = 80x + 28y + 100z subject to these constraints:

15x + 6y + 15z ≤ 960

30x + 6y + 15z ≤ 1500

25x + 20y + 25z ≤ 2250

10x + 4y + 20z ≤ 800

and the usual constraints x ≥ 0, y ≥ 0, z ≥ 0

The maximum value of P is and this occurs when x =

and y =

and z =

There is one slack variable with a non-zero value when the optimal solution is achieved. This slack variable is the slack variable introduced in constraint number ____ in the list of constraints (above), and the value this slack variable has when the optimal solution is achieved is ___.