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 X1X2 050 0

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) 12 + 3X2 = 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+7X2 1216136 455125=MIN 032224 050350

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+3X2 01236 3630=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+3X2 0824 1.74.720=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 100000X1+50000X2, X1=TV, X2= RADIO X2 X1 > 2 1000000X1+ 400000X2 > 3000000.6(1000000)X1+(1-.7)(40000)X2 1000000X1+400000X2 >.4 X1 < 5