Homework SourseLinear Algebra Help Maximize the function z x 3y subject t
Linear Algebra Help!!
Maximize the function z = x + 3y subject to the constraints: 3x + 7y lessthanorequalto 21, 3x + 2y s 12, x greaterthanorequalto 0, y greaterthanorequalto 0. Maximize the function z = x + y + 2w subject to the constraints: x + 2y - w lessthanorequalto 4, 3x + y + w lessthanorequalto 3, x greaterthanorequalto 0, y greaterthanorequalto 0, w greaterthanorequalto 0. Be sure to display the initial tableau, as well as any successive tableaus. At the end, list the values of all variables, including the slack variables. Check to see that those values agree with the objective function and the constraints.Solution
Maximize P = x +3y subject to
3x +7y<=21,
3x+2y <= 12,
x>=0,
y >=0
Tableau #1
x y s1 s2 s3 s4 p
3 7 1 0 0 0 0 21
3 2 0 1 0 0 0 12
1 0 0 0 -1 0 0 0
0 1 0 0 0 -1 0 0
-1 -3 0 0 0 0 1 0
Tableau #2
x y s1 s2 s3 s4 p
3 7 1 0 0 0 0 21
3 2 0 1 0 0 0 12
-1 0 0 0 1 0 0 0
0 1 0 0 0 -1 0 0
-1 -3 0 0 0 0 1 0
Tableau #3
x y s1 s2 s3 s4 p
3 7 1 0 0 0 0 21
3 2 0 1 0 0 0 12
-1 0 0 0 1 0 0 0
0 -1 0 0 0 1 0 0
-1 -3 0 0 0 0 1 0
Tableau #4
x y s1 s2 s3 s4 p
0.428571 1 0.142857 0 0 0 0 3
2.14286 0 -0.285714 1 0 0 0 6
-1 0 0 0 1 0 0 0
0.428571 0 0.142857 0 0 1 0 3
0.285714 0 0.428571 0 0 0 1 9
we get optimalsolutiuon as : P =9 ( maximum) ; x= 0 ; y = 3
