Construct the Dual and solve the Dual by the graphical and
simplex method.
Minimize Z = 1x1 + 2x2 + 3x3
Subject to:
0x1 + 6x2 + 2x3 >= J
3x1 + 2x3 + 5x3 >= K
x1, x2, and x3 >= 0
constant resources:
J = 25
K = 24
Please do on paper...
Construct the Dual and solve the Dual by the graphical and
simplex method.
Minimize Z = 1x1 + 2x2 + 3x3
Subject to:
0x1 + 6x2 + 2x3 >= J
3x1 + 2x3 + 5x3 >= K
x1, x2, and x3 >= 0
constant resources:
J = 25
K = 24
Construct the Dual and solve the Dual by the graphical and
simplex method.
Minimize Z = 1x1 + 1x2 + 2x3
Subject to:
2x1 + 2x2 + 1x3 >= J
5x1 + 6x2 + 7x3 >= K
x1, x2, and x3 >= 0
constant resources:
J = 15
K = 17
Please do on paper..
Given the following LP
max z = 2x1 + x2 + x3
s. t.
3x1 - x2 <= 8
x2 +x3 <= 4
x1,x3 >= 0, x2 urs (unrestricted in sign)
A. Reformulate this LP such that
1)All decision variables are non-negative.
2) All functional constraints are equality constraints
B. Set up the initial simplex tableau.
C. Determine which variable should enter the basis and which
variable should leave.
Find the optimum solution to the following LP using the Simplex
Algorithm. Use Two-Phase method.
??? ?=3?2+2?3 ??
−2?1 + ?2 − ?3 ≤ −3
−?1 + 2?2 + ?3 = 6
?1,?2,?3 ≥0
Find the optimum solution to the following LP using the Simplex
Algorithm. Use Big M method.
??? ?=5?1+2?2+?3 ??
?1 + ?2 ≤ 6
?1 − ?2 + 2?3 ≤ 2
3?1 + 2?2 = 12
?1,?2,?3 ≥0
Solve the following linear program using both the graphical and
the simplex methods:
Max
2X1
+ 8 X2
s.t.
3X1
+ 9X2
<=
15
2X1
+ X2
>=
12
X1, X2
>=
0
Show graphically how the simplex method moves from one basic
feasible solution to another. Find the coordinates of all extreme
points of the feasible region.
From the graphic I can see there's no solution , but how to
prove it through simplex method? Thank you!