Answers to set 3

1
Answers to set 3

• Set 4 due Thurs March 14
• Memo C-2 due Tues March 19
• Next exam Thurs April 4
• Tutor Mon 4-6PM, Thurs 2-4PM, BB 4120

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Problem 5

• X1ingred 1
• X2ingred 2
• Objective MIN cost 3x1 5x2
• Constraints
• 1)nitro 10x12x2 gt 20
• 2)phos 6x1 6x2 gt 36
• 3)potas x2 gt 2

3
5(contd)
4
5(contd)
5
5(contd)
6
x2
A
0,10
feasible
0,6
infeas
B
(1)
(2)
C
(3)
0,2
infeasible
infeasible
2,0
6,0
7
Corner pt B nitro, phos

• 10x12x220
• 6x16x236
• X11
• X25

8
Corner pt C Phos,potas

• 6x16x236
• X22
• X14

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Feasible corner points
10
MIN 3x15x2
11
Exam format

• Buy 4 pounds of ingredient 1 and 2 pounds of
  ingred 2 for 22 cost

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Problem 6

• X1chairs
• X2tables
• Obj max profit 400x1100x2
• Constr
• (1)labor 8x110x2 lt 80
• (2) wood 2x1 6x2 lt 36
• (3) demand x1 lt 6

13
x2
0,8
infeasible
0,6
A
B
feasible
infeasible
C
10,0
infeasible
18,0
6,0
D
14
Corner points
15
MAX 400x1100x2
16
Exam Format

• Make 6 chairs and 3.2 tables per day for 2720
  profit

17
Problem 7

• Plug optimal solution to 6 into labor constraint
  86103.280avail, so no labor slack
• Wood 2663.231.2lt36 avail, so wood slack
  36-31.24.8

18
Problem 8

• Re-do 6 with new table profit 500
• NEW objective function 400x1500x2

19
MAX 400x1500x2
20
Exam Format

• Sensitive to change since two corner points are
  now equally optimal

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Problem 24

• X1permanent
• X2temp
• Obj min cost 64x142x2
• Constr
• 1) claims 16x112x2 gt 450
• 2) computer station x1 x2 lt 40
• 3) defective .5x1 1.4x2 lt 25

22
x2
0,40
0,37
(1)
(2)
Infeasible
0,18
B
(3)
C
infeasible
28,0
50,0
A
40,0
D
23
Corner points
24
Min cost
25
Exam format

• Hire 20.12 permanent operators and 10.67
  temporary operators for cost of 1736
• Real world probably round up to 21 and 11 in
  anticipation of sick leave, attrition, etc

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Problem 25a

• Sensitivity on previous problem
• change objective function coefficient
• a change x1 coefficient

27
New cost 54x142x2
28
New min 1519

• X1gt0 only
• previous problem x1gt0 and x2gt0
• different corner pt
• no more temps
• solution sensitive to change

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25b change x2 coefficient

• Min cost 64x1 36x2

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(No Transcript)
31
25b insensitive

• Problem 24 corner pt B optimal
• Problem 25b corner pt B optimal
• same mix as 24

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26 Remove constraint from 24

• Remove constraint 3 (defective)

33
()
x2
3
0,40
0,37
Infeasible
(1)
(2)
Infeasible
0,18
B
C
infeasible
28,0
50,0
A
40,0
D
34
Problem 26
35
Problem 26 sensitive

• Problem 24 permanent and temp
• Problem 26 temp only
• New corner point