Simplex Method Consider the following linear programming
problem:
max
z = 6x1 + 3x2 - 9x2 - 9x3 + 15x4
s.t. 2x1 + 4x2 +6x3 + 8x4 <= 80
6x1
- 3x2 +3x3 + 6x4 <= 24
12x1 - 6x2 + 3x3 - 3x4 <= 30
x1,
x2, x3, x4 >= 0
Rewrite the problem in standard form, that is, add the necessary
slack variables in order to consider only equality constraints (and
non-negativity).
What is the...
Solve the following linear programming model graphically:
Max Z= 3x1 +4x2
Subject to: 2x1 + 4x2 <= 22
-x1 + 4x2 <= 10
4x1 – 2x2 <= 14 x1 – 3x2 <= 1
x1, x2, >=0
Clearly identify the feasible region, YOUR iso-profit line and
the optimal solution (that is, d.v. values and O.F. Value.
Consider the following integer linear
programming problem:
Max Z = 4.2x + 4.8y + 5.6z
Subject to: 4x + 2y + 7z ≤ 37
4x + 4y + 5z ≤ 40
2.8y ≤ 10
x,
y, z ≥ 0 and integer
What is the optimal solution to the integer
linear programming problem?
State the optimal values of decision variables.
Consider the following linear program. Maximize z= 5x1+ 3x2
subject to 3x1+ 5x2≤15
5x1+ 2x2≤10
– x1+ x2≤2
x2≤2.5
x1≥0, x2≥0
a. Show the equality form of the model.
b. Sketch the graph of the feasible region and identify the
extreme point solutions. From this representation find the optimal
solution.
c. Analytically determine all solutions that derive from the
intersection of two constraints or nonnegativity restrictions.
Identify whether or not these solutions are feasible, and indicate
the corresponding objective function...
consider the linear programming problem
maximize z = x1 +x2
subjected tp
x1 + 3x2 >= 15
2x1 + x2 >= 10
x1 + 2x2 <=40
3x1 + x2 <= 60
x1 >= 0, x2>= 0
solve using the revised simplex method and comment on any
special charateristics of the optimal soultion. sketch the feasible
region for the problem as stated above and show on the figure the
solutions at the various iterations
Max Z = 2x1 + 8x2 + 4x3
subject to
2x1 + 3x2 ≤ 8
2x2 + 5x3 ≤ 12
3x1 + x2 +
4x3
≤15
and x1,x2,x3≥0;
Indicate clearly the optimal basic and nonbasic
variables and their values and write the reduced cost of each
optimal nonbasic variable.
Consider the following linear optimization model.
Z = 3x1+ 6x2+ 2x3
st 3x1 +4x2 + x3 ≤2
x1+
3x2+ 2x3 ≤ 1
X1, x2, x3 ≥0
(10) Write the optimization problem in standard form with the
consideration of slack variables.
(30) Solve the problem using simplex tableau method.
(10) State the optimal solution for all variables.
Consider the following Integer Linear Programming (ILP)
model
Maximize Z = X1 + 4X2
Subject to X1 + X2 < 7 // Resource 1
–X1 + 3X2 < 3 // Resource 2
X1, X2 > 0
X1, X2 are integer
i. Consider using the Branch and Bound (B & B) technique to
solve the ILP model. With the
help of Tora software, draw the B & B tree. Always give
priority for X1 in branching over
X2. Clearly label the...