The simplex method can be used to find the maximum value of the following. P = 64x + 56y + 80z Subject to these constraints: 12x +12y + 12z 960 8x + 4y + 4z = 500 20x + 40y + 20z 2250 12x +12y + 24z 1200 and x 0, y 0, z 0 The maximum value of P is 5425 and this occurs when x = 40.63 X and y = 25.13 X and z = 15.63 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 constraints (above), and the value this slack variable has when the optimal solution is achieved is in the list of The simplex method can be used to find the maximum value of the following: P = 128x + 48y + 80z Subject to these constraints: 8x + 4y + 8z 400 16x + 4y + 8z 500 4x + 4y + 4z = 300 4x + 2y + 8z 400 and x 0, y = 0 I Z 0 The maximum value of P is 5150 and this occurs when x = 25/8 and y= = 125/4 X and z = 325/8 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 constraints (above), and the value this slack variable has when the optimal solution is achieved is in the list of