Apr 4 Exam: Two hours

1
Apr 4 Exam Two hours

• Everyone takes exam 400 to 600PM Thur
• Memo C-2 due Tues
• Set 5 due Thur March 21

2
Answers to set 4

• P 91, 5a
• X1basketballs
• X2footballs
• MAX 12x1 16x2
• Consr (1)(rubber) 3x12x2 lt 500
• (2) (leather)4x1 5x2 lt 800

3
P 91, Problem 6

• Continuation of problem 5
• Intercepts (1) 0,250 and 167,0
• (2) 0,160 and 200,0

4
x2
infeasible
0,250
0,160
A
(2)
128,57
B
infeasible
(1)
200,0
x1
167,0
C
(1
5
Corner pts
pt x1 x2 12x116x2
A 0 160 2560max
B 128.5 57.2 2457
C 167 0 2004
6
Exam format

• Make 160 footballs for 2560 profit

7
Part (a) slack

• CORNER PT A
• (1)(rubber)302160320lt500, so
  slack500-320180
  (2)(leather)405160800,no slack
• CORNER PT B zero slack
• CORNER PT C(1)no slack
  (2)4167668lt800, slack 800-668132

8
Part(b) Sensitivity

• Change in objective function
• Section 1 new basketball profit13

9
Corner pts
pt x1 x2 13x116x2
A 0 160 2560
B 128.5 57.2 2590max
C 167 0 2171
10
Section 1 sensitive

• Old optimum at pt A
• New optimum at pt B
• Start making basketballs

11
6bSection 2

• New football profit 15

12
Corner pts
pt x1 x2 12x115x2
A 0 160 2400max
B 128.5 57.2 2400max
C 167 0 2004
13
6b Section 2 tie

• Sensitive since optimum at A or B

14
6c constraint change

• Right-hand side of rubber constraint
• Section 1
• Old 500
• New 1000
• New (1) 3x12x2lt 1000
• New intercepts 0,500 and 333,0

15
x2
infeasible
0,500
0,160
A
(2)
New(1)
infeasible
infeasible
200,0
333,0
(1
16
Max profit
x1 x2 12x116x2
0 160 2560max
200 0 2400
17
6c Section 1insensitive

• Original solution 160 footballs
• New 160 footballs
• Same optimum

18
6cSection 2

• Right hand side of leather constraint
• Old 800
• New 1300
• New (2) 4x15x2 lt 1300
• New intercepts 0,260 and 325,0

19
0,260
infeasible
0,250
New(2)
infeasible
(1)
325,0
x1
167,0
C
(1
20
6c Section 2
x1 x2 12x116x2
0 250 4000max
167 0 2004
21
6cSection 2sensitive

• While output mix is same as original (footballs
  only), we must check slack to see if input
  sensitive
• Original problem pt A was optimum
• Rubber slackgt0, no leather slack
• New problem optimum on (1), so no rubber slack,
  but leather slackgt0, so input sensitive

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Set 4(3)Sensitivity range(Algebra)

• C1basketball profit
• objective function
• Z c1x116x2
• X2 (1/16)Z (C1/16)x1

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Constraint (1)

• (1) 3x12x2 500
• 2x2 500-3x1
• x2 250 1.5x1
• Set objective function coef of x1 constr
  (1) coef of x1
• C1/16 1.5, so C1 24
• Old C1 12, so C1 lt 24

24
Constraint (2)

• (2) 4x15x2 800
• X2 800/5 (4/5)x1
• Set objective function coef of x1
• constr (2) coef of x1
• C1/16 4/5 .8
• C1.816 12.8
• Old C112, so C1 lt 12.8

25
Answer C1 lt 12.8

• Answer must be in intersection of both ranges C1
  lt 24 and C1 lt 12.8
• ------------------------------------24
• ------------------12.8
• -------------12old C1

26
interpretation

• Make footballs only if unit basketball profit is
  less than 12.80
• But if unit basketball profit exceeds 12.80,
  start making basketballs
• Since current profit is 12.00, big change if
  unit profits increases by 80 cents