Question

Consider the following linear programming problem.

Maximize

P = 4x + 6y + 9z

subject to the constraints

2x | + | 3y | + | z | ≤ | 900 |

3x | + | y | + | z | ≤ | 350 |

4x | + | 2y | + | z | ≤ | 400 |

x ≥ 0, y ≥ 0, z ≥ 0

Write the initial simplex tableau.

x |
y |
z |
s_{1} |
s_{2} |
s_{3} |
P |
Constant |

900 | |||||||

350 | |||||||

400 | |||||||

0 |

Answer #1

Consider the following linear programming problem.
Maximize
P = 3x + 9y
subject to the constraints
3x + 8y ≤ 1
4x − 5y ≤ 4
2x + 7y ≤ 6
x ≥ 0, y ≥ 0
Write the initial simplex tableau.
x
y
s1
s2
s3
P
Constant
1
4
6
0

Use the simplex method to solve the linear programming
problem.
Maximize
P = 4x + 3y
subject to
3x
+
4y
≤
30
x
+
y
≤
9
2x
+
y
≤
17
x ≥ 0, y ≥ 0

Solve the linear programming problem by the method of
corners.
Maximize P = 2x + 6y
subject to 2x + y ≤ 16
2x + 3y ≤ 24
y ≤ 6
x ≥ 0, y ≥ 0
The maximum is P = at (x, y) = .

Use the simplex method to solve the linear programming
problem.
Maximize
P = 6x + 5y
subject to
3x
+
6y
≤
42
x
+
y
≤
8
2x
+
y
≤
12
x ≥ 0, y ≥ 0
The maximum is P =
at
(x, y) =

2. Solve the linear programming problem by the simplex
method.
Maximize 40x + 30y subject to the constraints:
x+y≤5
−2x + 3y ≥ 12
x ≥ 0, y ≥ 0

Solve the linear programming problem by the simplex method.
Maximize
P = 5x + 4y
subject to
3x
+
5y
≤
214
4x
+
y
≤
172
x ≥ 0, y ≥ 0
The maximum is P =
at (x, y) = .

Solve the linear programming problem by the method of corners.
Minimize C = 4x + 6y subject to 4x + y ≥ 38 2x + y ≥ 30 x + 3y ≥
30 x ≥ 0, y ≥ 0 The minimum is C = at (x, y) =

Solve the linear programming problem by the method of
corners.
Maximize
P = 2x + 3y
subject to
x
+
y
≤
10
3x
+
y
≥
12
−2x
+
3y
≥
11
x ≥ 0, y ≥ 0

Consider the following linear programming problem:
Maximize 12X + 10Y
Subject to:
4X + 3Y <= 480
2X + 3Y <= 360
all variables >= 0
The maximum possible value for the objective function is
Selected Answer:
c.
1520.

Consider the following linear programming model with 4 regular
constraints: Maximize 3X + 5Y subject to: 4X + 4Y ≤ 48 (constraint
#1) 2X + 3Y ≤ 50 (constraint #2) 1X + 2Y ≤ 20 (constraint #3) Y ≥ 2
(constraint #4) X, Y ≥ 0 (non-negativity constraints) (a) Which of
the constraints is redundant? Constraint #____. Justify using the
data from the above LP model:
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
(b) Is solution point (10,5) a feasible solution? _____. Explain
using...

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