Question

Consider the following mixed-integer linear program.

Max |
3x_{1} |
+ |
4x_{2} |
||

s.t. | |||||

4x_{1} |
+ |
7x_{2} |
≤ | 28 | |

8x_{1} |
+ |
5x_{2} |
≤ | 40 |

*x*_{1}, *x*_{2}
≥ and *x*_{1} integer

(c)

Find the optimal solution for the mixed-integer linear program. (Round your answers to three decimal places, when necessary.)

Answer #1

Problem 11-1
(a)
Indicate whether the following linear program is an all-integer
linear program or a mixed-integer linear program.
Max
30x1 + 25x2
s.t.
3x1 + 1.5x2 ≤ 400
1.5x1 + 2x2 ≤ 250
1x1 + 1x2 ≤ 150
x1, x2 ≥ 0
and x2 integer
This is a mixed-integer linear program.
Write the LP Relaxation for the problem but do not attempt to
solve.
If required, round your answers to one decimal place.
Its LP Relaxation is
Max
x1...

Consider the following LP problem:
Max 3X1 + 2X2
s.t.
5X1 + 4X2 £ 40
3X1 + 5X2 £ 30
3X1 + 3X2 £ 30
2X2 £ 10
X1 ³ 0, X2 ³ 0
(1) Show each constraint
and the feasible region by graphs. Indicate the feasible region
clearly. (5 points)
(2) Are there any
redundant constraints? If so, what constraint(s) is redundant? (2
points)
(3) Identify the optimal
point on your graph. What...

Solve the following linear program using the simplex method:
MAX
5X1
+ 5X2
+ 24X3
s.t.
15X1
+ 4X2
+ 12X3
<=
2800
15X1
+ 8X2
<=
6000
X1
+ 8X3
<=
1200
X1, X2, X3
>=
0

a. Solve the following linear programming model by using the
graphical method: graph the constraints and identify the feasible
region then determine the optimal solution (s) (show your
work).
Minimize Z = 3x1 + 7x2
Subject to 9x1 + 3x2 ≥ 36
4x1 + 5x2 ≥ 40
x1 – x2 ≤ 0
2x1 ≤ 13
x1, x2 ≥ 0
b. Are any constraints binding? If so, which one (s)?

Use a software program or a graphing utility to solve the system
of linear equations. (Round your values to three decimal places. If
there is no solution, enter NO SOLUTION. If the system has an
infinite number of solutions, set
x4 = t
and solve for x1, x2,
and x3 in terms of t.)
x1
−
2x2
+
5x3
−
3x4
=
23.3
x1
+
4x2
−
7x3
−
2x4
=
45.4
3x1
−
5x2
+
7x3
+
4x4
=...

Use a software program or a graphing utility to solve the system
of linear equations. (Round your values to three decimal places. If
there is no solution, enter NO SOLUTION. If the system has an
infinite number of solutions, set
x4 = t
and solve for x1, x2,
and x3 in terms of t.)
x1
−
2x2
+
5x3
−
3x4
=
23.3
x1
+
4x2
−
7x3
−
2x4
=
45.4
3x1
−
5x2
+
7x3
+
4x4
=...

Consider the following LP problem:
Minimize Cost = 3x1 +
2x2
s.t.
1x1 + 2x2 ≤ 12
2x1 + 3 x2 = 12
2 x1 + x2 ≥ 8
x1≥ 0,
x2 ≥ 0
What is the optimal solution of this LP?
(0,8)(12,0)(4,0)(0,4)(2,3)(0,6)(3,2)
I NEED SOLUTION!

Consider the following
LP: Max Z=X1+5X2+3X3
s.t. X1+2X2+X3=3
2X1-X2 =4 X1,X2,X3≥0
a.) Write the associated dual model
b.) Given the information that the optimal basic variables are
X1 and X3, determine the associated optimal dual solution.

Consider the following linear programming
problem.
Maximize 6X1
+ 4X2
Subject to:
X1
+ 2X2 ≤ 16
3X1
+ 2X2 ≤ 24
X1 ≥
2
X1,
X2 ≥ 0
Use Excel Solver to find the optimal values of X1 and
X2. In other words, your decision variables:
a.
(10, 0)
b.
(12, 2)
c.
(7, 5)
d.
(0, 10)

Consider the following linear program:
Max 3A + 2B
s.t
1A + 1B 10
3A + 1B < 24
1A + 2 B < 16
A, B > 0

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