Use the simplex method to solve the linear programming
problem.
Maximize objective function: Z= 6x1 + 2x2
Subject to constraints:
3x1 + 2x2 <=9
x1 + 3x2 <= 5
when x1, x2 >=0
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...
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...
Use the simplex method to solve the linear programming
problem.
Maximize
P = x + 2y + 3z
subject to
2x
+
y
+
z
≤
21
3x
+
2y
+
4z
≤
36
2x
+
5y
−
2z
≤
15
x ≥ 0, y ≥ 0, z ≥ 0
Use the simplex method to solve the linear programming
problem.
Maximize
P = 3x + 2y
subject to
3x
+
4y
≤
33
x
+
y
≤
9
2x
+
y
≤
13
x ≥ 0, y ≥ 0
The maximum is P = at
(x, y)
Use the simplex method to solve the linear programming
problem.
Maximize
P = 3x + 2y
subject to
3x
+
4y
≤
33
x
+
y
≤
9
2x
+
y
≤
13
x ≥ 0, y ≥ 0
The maximum is P = at
(x, y)
Use the simplex method to solve the linear programming
problem.
Maximize
P = x + 2y + 3z
subject to
2x
+
y
+
z
≤
56
3x
+
2y
+
4z
≤
96
2x
+
5y
−
2z
≤
40
x ≥ 0, y ≥ 0, z ≥ 0
The maximum is P = at
(x, y, z) =
Use the simplex method to solve the linear programming
problem.
Maximize
P = x + 2y + 3z
subject to
2x
+
y
+
z
≤
28
3x
+
2y
+
4z
≤
48
2x
+
5y
−
2z
≤
20
x ≥ 0, y ≥ 0, z ≥ 0
The maximum is P = ________
at
(x, y, z) = (_______)
.
Use the simplex method to solve the linear programming
problem.
Maximize
P = 4x + 3y
subject to
3x
+
6y
≤
33
x
+
y
≤
7
3x
+
y
≤
19
x ≥ 0, y ≥ 0
The maxium P= ____ at (x,y) ____