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

###### Question details

Use the simplex method to find the maximum value of P = 160x + 96y + 40z subject to these constraints:

15x + 12y + 6z ≤ 600

10x + 4y + 2z ≤ 250

5x + 8y + 2z ≤ 300

25x + 20y + 20z ≤ 2000

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 __(4)___ in the list of constraints (above), and the value this slack variable has when the optimal solution is achieved is ____