In: Advanced Math

Solve the following linear integer programming model using the Cutting Plane method. Show all relevant work in your solution report.

*Maximize Z = x*1 + *x*2

*Subject to*

3*x*1 + 2*x*2 < 5

*x*2 < 2

*x*1, *x*2 > 0 and integer.

Maximization by the simplex method
Solve the following linear programming problems using the
simplex method.
1>.
Maximize z = x1 + 2x2 +
3x3
subject to x1 + x2 +
x3 ≤ 12
2x1 + x2 + 3x3 ≤ 18
x1, x2, x3 ≥ 0
2>.
A farmer has 100 acres of land on which she plans to grow wheat
and corn. Each acre of wheat requires 4 hours of labor and $20 of
capital, and each acre of corn...

QUESTION 1: Solve the linear programming model given below using
the simplex method. Write the primal and dual results from the
optimal table you obtained.
MAX Z = 10?1 + 20?2 + 5?3
6?1 + 7?2 + 12?3 ≥ 560
5?1 − 3?2 + x3 ≤
100
2000?1 + 1000?2 + 1000?3 ≤
62298
?1,?2,?3 ≥ 0
IMPORTANT REMINDER ABOUT THE QUESTION SOLUTION: NEW ORDER
CALCULATIONS SHOULD BE WRITTEN DETAILED WHEN CREATING THE SYMPLEX
TABLES. WHEN THE CALCULATIONS ARE SHOWED AND...

Solve the following linear programming problem using the dual
simplex method:
max ? = −?1 − 2?2
s.t.
−2?1 + 7?2 ≤ 6
−3?1 + ?2 ≤ −1
9?1 − 4?2 ≤ 6
?1 − ?2 ≤ 1
7?1 − 3?2 ≤ 6
−5?1 + 2?2 ≤ −3
?1,?2 ≥ 0

Use the simplex method to solve the following linear programming
problems. Clearly indicate all the steps, the
entering and departing rows and columns and rows, the pivot
and the row operations used. An investor has up to
N$450,000 to invest in three types of investments. Type A pays 6%
annually and has a risk factor of 0. Type B pays 10% annually and
has a risk factor of 0.06. Type C pays 12% annually and has a risk
factor of...

Use the dual simplex method to solve the following linear
programming problems. Clearly indicate all the steps, the entering
and departing rows and columns and rows, the pivot and the row
operations used. Use the simplex method to solve the following
linear programming problems. Clearly indicate all the steps, the
entering and departing rows and columns and rows, the pivot and the
row operations used. 2.2.1 An electronics manufacturing company has
three production plants, each of which produces three different...

SOLVE THE FOLLOWING 2 LINEAR PROGRAMMING PROBLEMS USING
EXCEL AND THE SOLVER ADD-IN. PLEASE SHOW ME ALL THE EXCEL
STEPS.
PROBLEM #1: Maximize Z = $60X +
$90Y
Subject to: 60X + 30Y >= 1,500
100X + 100Y <= 6,000
Y >= 30
X, Y >= 0
PROBLEM #2: Minimize Z = $3,000X + $1,000Y
Subject to: 60X + 20Y >=
1,200
10X + 10Y >=
400
...

Developing a workforce schedule (using Linear Programming to
model and solve this problem)
A local bank needs the minimum number
of employees needed for each day of the week listed in the
following table. If a staff is hired, his/her schedule will be
working 5 consecutive days and take two days off. The bank operates
seven days a week.
Day of the Week
M
T
W
TH
F
Sa
Su
Number of staff needed
4
5
5
3
5
2...

Consider the following transportation problem. Formulate this
problem as a linear programming model and solve it using the MS
Excel Solver tool.
Shipment Costs ($), Supply, and
Demand:
Destinations
Sources
1
2
3
Supply
A
6
9
100
130
B
12
3
5
70
C
4
8
11
100
Demand
80
110
60
(4 points) Volume Shipped from Source A __________
(4 points) Volume Shipped from Source B __________
(4 points) Volume Shipped from Source C __________
(3 points) Minimum...

Formulate the problem as a linear programming model use excel
and show your excel work. Thank you.
To (cost, in 100's)
From
New york
Philadelphia
Chicago
Boston
Supply
Tampa
$9
$14
$12
$17
200
Miami
11
10
6
10
200
Fresno
12
8
15
7
200
Demand
130
170
100
50

Solve this linear programming (LP) problem using the
transportation method. Find the optimal transportation plan and the
minimum cost. (Leave no cells blank - be certain to enter
"0" wherever required. Omit the "$" sign in your
response.)
Minimize
8x11
+
2x12 + 5x13 +
2x21 + x22
+ 3x23 +
7x31 + 2x32 +
6x33
Subject to
x11 + x12 +
x13
=
90
x21 + x22 +
x23
=
105
x31 + x32 +
x33
=
105
x11...

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