solve the indicated linear programming problem using simplex

solve the indicated linear programming problem using simplex method

Minimize z - 3x + 2y subject to the constraints

2x+ y<4

3x- 2y < 6

x>_0, y>_0.

Please explain clearly. Thanks :)

Solution

Minimize z = 3x+2y is equivalent to Maximize -z = -3x-2y

Now The problem reduces to:

Maximize -3x-2y subject to

2x+y<4

3x-2y<6

x>=0, y>=0

Standard form:

Maximize -3x-2y+0s₁+0s₂

2x+y+s₁ = 4

3x-2y +s₂=6

x>=0, y>=0, s₁>=0, s₂>=0

Initial basic feasible solution:

x=0, y=0, s₁=4, s₂ =6

Simplex Table:

The bottom row has all entries positive and hence this is condition for optimal solution

So the optimal solution to the above problem is :

(x,y) = (0,0)

Als0 z = 0+0 = 0