ASSIGNMENTS GROUP MEMBERS: CHAPTER(S) & PROBLEM(S): Fatema Choukeir 7-24 & 9-11 Lina Idelbti 7-27 & 8-24 James Kim 7-38 & 9-5 Anthony Cangialosi 7-41 Bruno Silva 8-27 & 9-8 Akintundo Oyauwusi 9-17 Christopher Raines 7-53 Anisha Patel 9-2 & 9-17 Nisorg Patel 8-30 Paula Dunn 7-50 & 8-21 Adetola Poppoola 9-23 Justin A Conyers 7-30 & 9-14
Justin A. Conyers Chapter 7-30 A: !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: 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 !DEMAND CONSTRAINT FOR YEAR ENDING INVENTORY; H >= 500; !MAXIMUM PRODUCTION CAPACITY CONSTRAINT FOR QUARTER 1; A <= 4000; !MAXIMUM PRODUCTION CAPACITY CONSTRAINT FOR QUARTER 2; B <= 3000; !MAXIMUM PRODUCTION CAPACITY CONSTRAINT FOR QUARTER 3; C <= 2000; !MAXIMUM PRODUCTION CAPACITY CONSTRAINT FOR QUARTER 4; D <= 4000; !NON-NEGATIVITY CONSTRAINS; A >= 0; B >= 0; C >= 0; D >= 0; END
Justin A. Conyers Chapter 9-14 B: QUARTERNUMBER OF BOATS PRODUCED INVENTORY CLOSE OF QUARTER ASSOCIATED COSTS 140002100$40,525,000.00 230001100$33,275,000.00 32000100$24,230,000.00 419005000$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 4 th quarter there is a zero dual cost meaning that there is room to produce more in the 4 th 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: