Question

How do i generate a gomory cut from this optimal dictionary form, expressing all the cuts in terms of the variables x1 and x2:

max 15 - 4x3 - 2x4

s.t. x1 = 11/4 - (5/2)x3 + (1/4)x4

x2 = 2 + 2x3

x1, x2, x3, x4 >= 0

Answer #1

x1 + (5/2)x3 - (1/4)x4 = 11/4

or, (1+0)x1 + (2+ 1/2)x3 + (-1 + 3/4)x4 = (2 + 3/4)

Now consider the fractional parts only and replace the = sign with >=

**(1/2)x3 + (3/4)x4 >= 3/4** which is the Gomory
cut equation

In the tableau, it will become, **(1/2)x3 + (3/4)x4 + G =
3/4** i.e. we will write a slack term G to establish
equality for the tableau.

---------------------------------------

x2 - 2x3 = 2

or, (1+0) + (-2+0)x3 = (2+0)

If we consider the fractional parts here, we will get 0+0=0; so
no cut eqaution can be generated here.

what is the dual problem?
MAX 100X1+120X2+150X3+125X4
S.T.
1) X1 + 2X2 + 2X3 + 2X4 ≤ 108
2) 3X1 + 5X2 + X4 ≤ 120
3) X1 + X3 ≤ 25
4) X2 + X3 + X4 ≥ 50
X1,X2,X3,X4≥0

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...

STAR Co. provides paper to smaller companies whose volumes are
not large enough to warrant dealing directly with the paper mill.
STAR receives 100-feet-wide paper rolls from the mill and cuts the
rolls into smaller rolls of widths 12, 15, and 30 feet. The demands
for these widths vary from week to week. The following cutting
patterns have been established:
Number of:
Pattern
12ft.
15ft.
30ft.
Trim Loss
1
0
4
1
10 ft.
2
4
3
0
7 ft....

STAR Co. provides paper to smaller companies whose volumes are
not large enough to warrant dealing directly with the paper mill.
STAR receives 100-feet-wide paper rolls from the mill and cuts the
rolls into smaller rolls of widths 12, 15, and 30 feet. The demands
for these widths vary from week to week. The following cutting
patterns have been established:
Number of:
Pattern
12ft.
15ft.
30ft.
Trim Loss
1
5
0
1
10 ft.
2
0
0
3
10 ft....

STAR Co. provides paper to smaller companies whose volumes are
not large enough to warrant dealing directly with the paper mill.
STAR receives 100-feet-wide paper rolls from the mill and cuts the
rolls into smaller rolls of widths 12, 15, and 30 feet. The demands
for these widths vary from week to week. The following cutting
patterns have been established:
Number of:
Pattern
12ft.
15ft.
30ft.
Trim Loss
1
5
0
1
10 ft.
2
0
0
3
10 ft....

Consider the following linear program Max 5x1+5x2+3x3
St
x1+3x2+x3<=3
-x1+ 3x3<=2
2x1-x2 +2x3<=4
2x1+3x2-x3<=2
xi>=0 for i=1,2,3
Suppose that while solving this problem with Simplex method, you
arrive at the following table:
z
x1
x2
x3
x4
x5
x6
x7
rhs
Row0
1
0
-29/6
0
0
0
11/6
2/3
26/3
Row1
0
0
-4/3
1
0
0
1/3
-1/3
2/3
Row2
0
1
5/6
0
0
0
1/6
1/3
4/3
Row3
0
0
7/2
0
1
0
-1/2
0...

1. Consider the general form of the utility for goods that are
perfect complements.
a) Why won’t our equations for finding an interior solution to the
consumer’s problem work for this kind of utility? Draw(but do not
submit) a picture and explain why (4, 16) is the utility maximizing
point if the utility is U(x, y) = min(2x, y/2), the income is $52,
the price of x is $5 and the price of y is $2. From this picture
and...

I have solved the problem up to number 6. all my answers
from 7 keeps coming up incorrect. That is where i need the help.
Thank you
Note: This problem is for the 2018 tax
year.
Daniel B. Butler and Freida C. Butler, husband and wife, file a
joint return. The Butlers live at 625 Oak Street in Corbin, KY
40701. Dan's Social Security number is 111-11-1112, and Freida's is
123-45-6789. Dan was born on January 15, 1967, and Freida...

1) What are some indicators that there are assignable
causes for variation in a process?
I.Process capability.
II. Data patters outside of the control limits.
III. Data patters within the control limits.
IV. Points randomly falling above and below the control chart
center line.
a.
II and III
b.
II, III, IV
c.
I, II, IV
d.
I, II, III, IV
2) The best quantitative tool to determine the cause for
variation in a process is:
a.
ANOVA
b.
Correllation...

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