Tutor Tues Apr 2, 2-4 PM since no classes Apr 1

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 gt96
X1 X2
0 96/332
96/424 0
5
X2
0,32
(1)
X1
24,0
6
(2) X1 X2 lt50
X1 X2
0 50
50 0
7
X2
0,50
0,32
(2)
(1)
X1
50,0
24,0
8
(3) X1 3X2 gt60
X1 X2
0 60/320
60 0
9
X2
0,50
0,32
(2)
(1)
0,20
(3)
X1
50,0
60,0
24,0
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
X2
Corner points
0,50
0,32
(2)
(1)
0,20
Not feasible
12,16
45,5
(3)
X1
50,0
60,0
24,0
Not feasible
13
MINIMUM COST
X1 X2 2X17X2
12 16 136
45 5 125MIN
0 32 224
0 50 350
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
3,6
0,3
INFEASIBLE
6,0
INFEASIBLE
18
MINIMIZE COST
X1 X2 COST 4X13X2
0 12 36
3 6 30MIN
19
ORIGINAL PROBLEM

• MAKE BOTH X1 AND X2

20
NEW PROBLEM

• CHANGE (1) 2X1X2 gt8

21
0,12
0,8
3,6
1.7,4.7
0,3
4,0
6,0
INFEASIBLE
22
MIN COST
X1 X2 COST 4X13X2
0 8 24
1.7 4.7 20MIN
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 lt 24

28
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 lt 6
• STEP 3 C1 lt 24
• ANSWER C1 lt 6

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(4) MAX X13X22X34X4

• X1AM PHONE, X2AM RIDE, X3AFT PHONE, X4AFT
  RIDE
• CONSTRAINTS
• AM X120X2 lt 12(60)720
• AFT 2X330X4 lt 14(60) 840
• GAS X2X4 lt 100

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(5)MIN 3X14X22X3X4, X1FISH,X2BEEF,
X3LETTUCE, X4BEANS

• CAL 1000lt400X1700X240X3500X4lt1800
• FAT 15lt4X180X22X4lt40
• PROT 90X1100X22X320X4gt25
• CHOL 100X1300X2lt19

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(6)MIN 100000X150000X2, X1TV, X2 RADIO

• X2
  
  X1 gt 2
• 1000000X1 400000X2 gt 3000000
• .6(1000000)X1(1-.7)(40000)X2
  1000000X1400000X2 gt
  .4
• X1 lt 5