Question

Maximize For the given maximization problem, (a) determine the number of slack variables needed, (b) name them, and (c) use slack variables to convert each constraint into a linear equation. subject to: z = 10x4 + 3x2 + x3 6x7 + 8x2 +9X3 S 134 2X2 + 5x2 + 12x3 s 225 X120, X220, + a. How many slack variables are needed? with Xzzo

Answer 1

Problem is

Max Z = 10 x1 + 3 x2 + x3

subject to

6 x1 + 8 x2 + 9 x3 ≤ 134 2 x1 + 5 x2 + 12 x3 ≤ 225

and x1,x2,x3≥0;

The problem is converted to canonical form by adding slack, surplus and artificial variables as appropiate

1. As the constraint-1 is of type '≤' we should add slack variable S1

2. As the constraint-2 is of type '≤' we should add slack variable S2

a) Hence total number of slack variable is 2.

b) name are S1 and S2

c) After introducing slack variables to convert constraint into linear equation:

Max Z = 10 x1 + 3 x2 + x3 + 0 S1 + 0 S2

subject to

6 x1 + 8 x2 + 9 x3 + S1 = 134 2 x1 + 5 x2 + 12 x3 + S2 = 225

and x1,x2,x3,S1,S2≥0