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
maximize z = 2x1+3x2
subject to x1+3X2 6
3x1+2x2 6
x1,x2
This can be simply done by drawing all the lines in the x-y
plane and looking at the corner points.
Our points of interest are the corner points and we will check
where we get the maximum value for our objective function by
putting all the four corner points. (2,0), (0,2), (0,0), (6/7,
12/7)
We get maximum at = (6/7, 12/7) and the maximum value is =...
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.