OM-375 GROUP LINGO
QUIZ #1: CHAPTERS 7, 8, & 9
AND STOCK DATA.
ASSIGNED PROBLEMS
• CHAPTER 7: 24 27 30 38 41 50 53
• CHAPTER 8: 21 24 27 30
• CHAPTER 9: 2 5 8 11 14 17 20 23
ASSIGNMENTS
GROUP MEMBERS:
Fatema Choukeir
Lina Idelbti
James Kim
Anthony Cangialosi
Bruno Silva
Akintundo Oyauwusi
Christopher Raines
Anisha Patel
Nisorg Patel
Paula Dunn
Adetola Poppoola
Justin A Conyers
CHAPTER(S) & PROBLEM(S):
7-24 & 9-11
7-27 & 8-24
7-38 & 9-5
7-41
8-27 & 9-8
9-17
7-53
9-2 & 9-17
8-30
7-50 & 8-21
9-23
7-30 & 9-14
Justin A. Conyers Chapter 7-30 A:
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!Justin A. Conyers;
!OM 375 Dr. Lawrence;
!Problem 7-30 Data entered into Lingo:
!MAXIMIZE TOTAL RETURN (ASSUMING INCREASE IN STOCK PRICE);
MAX = E*15 + C*18;
!CONSTRAINT ON MAXIMUM INVESTMENT;
40*E + 25*C <= 50000;
!CONSTRAINT ON MINIMUM INVESTMENT IN EASTERN CABLE (E);
40*E >= 15000;
!CONSTRAINT ON MINIMUM INVESTMENT IN COM SWITCH (C);
25*C >= 10000;
!CONSTRAINT PREDICATED ON RISK IN INVESTING IN COM SWITCH (C);
25*C <= 25000;
!NON-NEGATIVITY CONSTRAINT;
E >= 0;
C >= 0;
END
Justin A. Conyers Chapter 7-30 A contd:
Justin A. Conyers Chapter 7-30 c:
• The coordinates of each extreme point are
as follows:
• (375, 1000)
• (375, 400)
• (1000, 400)
• (625, 1000)
• Excluding the extreme points where either
value would be set to zero considering that
the constraints in this problem allots for a
minimum of 10000 dollars in Comstock and
15000 in Eastern stock.
Justin A. Conyers Chapter 7-30 d:
• The optimal solution in this problem is
to invest in 625 shares of Eastern
Cable stock as well as to invest in 1000
shares of ComSwitch stocks to meet
the constraints and investment
maximization of the client.
• The return on the total investment
shall be $27375.00
Justin A. Conyers Chapter 9-14 A:
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The linear programming model was formed in Lingo:
!OM 375 Dr. Lawrence;
!Problem 9-14;
!MINIMIZE TOTAL COSTS ASSOCIATED WITH MANUFACTURING STORING
AND MAINTAINING INVENTORY;
! A B C D REPRESENT NUMBER OF BOATS PRODUCED PER QUARTER E F G H
REPRESENT ENDING INVENTORY OF BOATS PER QUARTER;
MIN = A*10000 + B*11000 + C*12100 + D*13310 + E*250 + F*250 +
G*300 + H*300;
!DEMAND CONSTRAINT FOR 1ST QUARTER;
A - E = 1900;
!DEMAND CONSTRAINT FOR 2ND QUARTER;
E + B - F = 4000;
!DEMAND CONSTRAINT FOR 3RD QUARTER;
F + C - G = 3000;
!DEMAND CONSTRAINT FOR 4TH QUARTER;
G + D - H = 1500;
Justin A. Conyers Chapter 9-14 A: cont’d
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!DEMAND CONSTRAINT FOR YEAR ENDING INVENTORY;
H >= 500;
!MAXIMUM PRODUCTION CAPACITY CONSTRAINT FOR QUARTER
A <= 4000;
!MAXIMUM PRODUCTION CAPACITY CONSTRAINT FOR QUARTER
B <= 3000;
!MAXIMUM PRODUCTION CAPACITY CONSTRAINT FOR QUARTER
C <= 2000;
!MAXIMUM PRODUCTION CAPACITY CONSTRAINT FOR QUARTER
D <= 4000;
!NON-NEGATIVITY CONSTRAINS;
A >= 0;
B >= 0;
C >= 0;
D >= 0;
1;
2;
3;
4;
Justin A. Conyers Chapter 9-14 B:
QUARTER
NUMBER OF
BOATS
PRODUCED
INVENTORY
CLOSE OF
QUARTER
ASSOCIATED
COSTS
1
4000
2100
$40,525,000.00
2
3000
1100
$33,275,000.00
3
2000
100
$24,230,000.00
4
1900
5000
$25,439,000.00
TOTAL:
$123,469,000.0
Justin A. Conyers Chapter 9-14 C:
C: The dual price as learned in Chapter 8,
refers to the improvement in the value of the
optimal solution when we increase the right
hand side of a constraint by one unit. As a
manager this is important to quantify the
potential risk and/or loss associated with an
increase in production. My advice would be to
only increase production in any quarter if the
dual price is below the next quarter’s
associated costs considering a 10% increase
quarterly.
Justin A. Conyers Chapter 9-14 D:
D: In the 4th quarter there is a zero dual
cost meaning that there is room to produce
more in the 4th quarter. Quarters 1
through 3 have positive dual prices, in
consideration of this fact we can improve
upon the objective function by increasing
production. For each additional unit
produced the cost associated with
producing the boat(s) will decrease the
total costs by the same amount.
Justin A. Conyers Chapter 9-14
Lingo screen shot: