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

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Answers to Practice Problems II Problem (1)

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

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X1 X2 0,32 24,0 (1)

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(2) X1 + X2 <50 X1X

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

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

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

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

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

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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

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MINIMUM COST X1X22X1+7X =MIN

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

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ANSWER: (2)

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

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

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MINIMIZE COST X1X2COST= 4X1+3X =MIN

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ORIGINAL PROBLEM MAKE BOTH X1 AND X2

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

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

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MIN COST X1X2COST= 4X1+3X =MIN

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

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

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

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

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

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

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

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(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

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(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

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(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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