Question

**** Linear Programming
****

Max Z = 6x_{1} +
10x_{2}+9x_{3} + 20x_{4}

constraint

4x_{1} + 9x_{2} + 7x_{3} + 10x_{4}
= 600

x_{1} + x_{2}+3x_{3} + 40x_{4}=
400

3x_{1} + 4x_{2} + 2x_{3} + x_{4} =
500

x_{1},x_{2},x_{3} ,x4 ≥ 0

**Find the allowable decrease
and increase for x4.**

Answer #1

** Linear Programming
**
max 6x1 +
10x2+9x3 + 20x4
Subject to
4x1 + 9x2 + 7x3 + 10x4
≤ 600
x1 + x2 +3x3 + 40x4 ≤
400
3x1+ 4x2 + 2x3 + x4 ≤
500
x1,x2,x3,x4 ≥ 0
List all the complementary
slackness equations.

Solve the linear programs using the simplex tableau.
Max
Z = -6X1 - 14X2 - 13X3
Subject to X1 +
4X2 + 2X3 ≤ 48
X1 + 2X2 + 4X3 ≤ 60
X1, X2, X3 ≥ 0

Consider the following integer programming problem.Maximize:
z=8x1 +12x2 +6x3
+4x4
Subject to constraint: 5x1 + 9x2
+4x3 +3x4 ≤ 16 where x1, x2, x3 and x4 are
binary integers (0 or 1).
By applying the Branch and Bound Algorithm find the
solution.

Find the duals of the following LP:
max z = 4x1 - x2 + 2x3
s.t. x1 + x2 <= 5
2x1 + x2 <= 7
2x2 + x3 >= 6
x1 + x3 = 4
x1 >=0, x2, x3 urs
show steps

The following is the mathematical model of a linear programming
problem for profit:
Maximize Z = 2X1 + 3X2
subject to:
4X1 + 9X2 ≤ 72
10X1 + 11X2 ≤ 110
17X1 + 9X2 ≤ 153
X1 , X2 ≥ 0
The constraint lines have been graphed below along with one example
profit line (dashed). The decision variable X1 is used as the X
axis of the graph.
Which of the following gives the constraint line that cuts the
X2...

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 mixed-integer linear program.
Max
3x1
+
4x2
s.t.
4x1
+
7x2
≤
28
8x1
+
5x2
≤
40
x1, x2
≥ and x1 integer
(c)
Find the optimal solution for the mixed-integer linear program.
(Round your answers to three decimal places, when necessary.)

Maximize 12X1 + 10X2 + 8X3
Total Profit
Subject to X1 + X2 + X3 >
160 At least a total of
160 units of all three products needed
X1
+ 3X2 + 2X3 ≤ 450
Resource 1
2X1 + X2 +
2X3 ≤ 300 Resource
2
2X1 + 2X2 + 3X3 ≤
400 Resource 3
And X1,
X2, X3 ≥ 0
Where X1, X2, and X3 represent the number of units of Product 1,
Product...

The following is the mathematical model of a linear programming
problem for profit:
Maximize subject to
Z = 2X1 + 3X2
4X1+9X2 ≤ 72 10X1 + 11X2 ≤ 110 17X1 + 9X2 ≤ 153
X1 , X2 ≥ 0
The constraint lines have been graphed below along with one
example profit line (dashed). The decision variable X1 is used as
the X axis of the graph. Use this information for questions
19 through 23.
A). Which of the following gives...

Solve the linear systems that abides by the following rules.
Show all steps.
I. The first nonzero coefficient in each equation is one.
II. If an unknown is the first unknown with a nonzero
coefficient in some equation, then that unknown doesn't appear in
other equations.
II. The first unknown to appear in any equation has a larger
subscript than the first unknown in any preceding equation.
a. x1 + 2x2 - 3x3 + x4 = 1.
-x1 - x2...

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