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Tutor Tues Apr 2, 2-4 PM since no classes Apr 1 Set 6 due Apr 9 Set 7 due April 11 C-3 due April 18.

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Presentation on theme: "Tutor Tues Apr 2, 2-4 PM since no classes Apr 1 Set 6 due Apr 9 Set 7 due April 11 C-3 due April 18."— Presentation transcript:

1 Tutor Tues Apr 2, 2-4 PM since no classes Apr 1 Set 6 due Apr 9 Set 7 due April 11 C-3 due April 18

2 Typo: Summer Schedule Page 27, MSCI 306M Session 1: June 3-July 12 (6 weeks)

3 Answers to Practice Problems II Problem (1)

4 (1) 4X1 + 3X2 >96 X1X2 096/3=32 96/4=240

5 X1 X2 0,32 24,0 (1)

6 (2) X1 + X2 <50 X1X

7 X1 X2 0,32 24,0 0,50 50,0 (1) (2)

8 (3) X1 +3X2 >60 X1X2 060/3=20 600

9 X1 X2 0,32 24,0 0,50 50,0 (1) (2) 0,20 60,0 (3)

10 Corner Point: (1),(3) (1) 4X1 + 3X2 = 96 (3) X1 + 3X2 = 60 (1)-(3) 3X1 = 36 X1 = 12 (3) X2 = 60, so X2 = 16

11 Corner Point: (2),(3) (2) X1 + X2 = 50 (3) X1 + 3X2 = 60 (3)-(2) 2X2= 10 X2 = 5 (2) X1 + 5 = 50 X1 = 45

12 X1 X2 0,32 24,0 0,50 50,0 (1) (2) 0,20 60,0 (3) Corner points Not feasible Not feasible 12,16 45,5

13 MINIMUM COST X1X22X1+7X =MIN

14 EXAM FORMAT MAKE 45 UNITS OF ALASKA AND 5 UNITS ARABIAN FOR $ 125 COST

15 ANSWER: (2)

16 SIMULTANEOUS EQUATIONS (1)2X1 + X2 = 12 (2) X1 – X2 = -3 (1)+(2)3X1 = 9 X1 =3 3-X2 = -3 X2 = 6

17 0,12 6,0 0,3 3,6 INFEASIBLE

18 MINIMIZE COST X1X2COST= 4X1+3X =MIN

19 ORIGINAL PROBLEM MAKE BOTH X1 AND X2

20 NEW PROBLEM CHANGE (1) 2X1+X2 >8

21 0,12 6,0 0,3 3,6 INFEASIBLE 0,8 4,0 1.7,4.7

22 MIN COST X1X2COST= 4X1+3X =MIN

23 OUTPUT INSENSITIVE NEW: MAKE BOTH X1 AND X2 ALSO INPUT INSENSITIVE SINCE BOTH ORIGINAL PROBLEM AND NEW PROBLEM HAVE NO SLACK

24 (3) ALGEBRA STEP 1: OBJECTIVE FUNCTION OLD C1 = 5

25 Z= C1X1 +12X2 12X2 = Z – 5X1 X2 = (1/12)Z – (C1/12)X1 COEFFICIENT OF X1 IS –C1/12

26 STEP 2: CONSTRAINT (1) 2X1 + X2 = 200 X2 = 200 –2X1 COEF OF X1 IS -2

27 STEP 3: STEP 1 = STEP 2 -C1/12 = -2 C1 = 24 OLD C1 = 5 C1 < 24

28 STEP 4: CONSTRAINT (2) X1 + 2X2 = 300 2X2 = 300 –X1 X2 = 150 –0.5 X1 COEF OF X1 IS –0.5

29 STEP 5: STEP 1 = STEP 4 -C1/12 = -0.5 C1 = 6 OLD C1 = 5 C1 < 6 STEP 3: C1 < 24 ANSWER: C1 < 6

30 (4) MAX X1+3X2+2X3+4X4 X1=AM PHONE, X2=AM RIDE, X3=AFT PHONE, X4=AFT RIDE CONSTRAINTS AM: X1+20X2 < 12(60)=720 AFT: 2X3+30X4 < 14(60) = 840 GAS: X2+X4 < 100

31 (5)MIN 3X1+4X2+2X3+X4, X1=FISH,X2=BEEF, X3=LETTUCE, X4=BEANS CAL: 1000<400X1+700X2+40X3+500X4<1800 FAT: 15<4X1+80X2+2X4<40 PROT: 90X1+100X2+2X3+20X4>25 CHOL: 100X1+300X2<19

32 (6)MIN X X2, X1=TV, X2= RADIO X2 X1 > X X2 > ( )X1+(1-.7)(40000)X X X2 >.4 X1 < 5


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