UNIT 3 DECISIONAL TREE MANAGEMENT SCIENCE PDF

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Summary

PRACTICE PROBLEMS AND ANSWERS THAT WOULD HELP STUDENTS WHO ARE STRUGGLING IN THIS COURSE SPECIFICALLY WHEN IT COMES TO DECISION MAKING...

Description

Activity no. 2 Problem_1:

A

Contract awarded P=0.5

B

Prepare a bid

0

awarded P=0.5

-10,000

Contract awarded

Prepare a bid 68,200 Not

Success P=0.8

Contract not

Not prepare

A

C

0

P=0.5

Failure P=0.2

200,000 -10,000

-18,000 - 10,000

Success 146,400

P=0.8

Contract not awarded -10,000

Failure P=0.2

190,000

-28,000

P=0.5 Solutions: Position B: EV = 0.5 (146,400) + 0.5 (-10,000) = 73,200 – 5,000 = 68,200 Position C: EV = 0.8 (190,000) + 0.2 (-28,000) = 152,000 – 5,600 = 146,400 Position A: Final Alternatives Prepare a bid = ₱68,200 Not = 0

The final alternatives are ₱68,200 and 0 Decision: The manager should prepare the bid and expect a payof of ₱62,800.

Problem_2

Electronic system Cost: -₱60,000

C

Success 800,000 P = 0.65 -60,000 - 75,000

Purchase patent

A

Cost: -₱75,000

Not

B

Failure

0

P = 0.35

0 Manual system Cost: -₱40,000

Success

D

-60,000 - 75,000 800,000

P = 0.75

-40,000 - 75,000

Failure P = 0.25

Electronic system Cost: -₱60,000

A

385,000

Success

0 -40,000 - 75,000

665,000

P = 0.65

Purchase patent Cost: -₱75,000

Not

485,000

Failure - 135,000 P = 0.35

0 Manual system Cost: -₱40,000

485,000

Success P = 0.75

685,000

Failure - 115,000 P = 0.25

Solutions: Position C: Electronic System Success Success Electronic (cost) Patent (cost) Total

800,000 -60,000 -75,000 665,000

Failure Electronic (cost) -60,000 Patent (cost) -75,000 Total -135,000

EV = 0.65 (665,000) + 0.35 (-135,000) = 432,250 – 47,250 = 385,000

Position D: Manual System Success Success Electronic (cost) Patent (cost) Total

800,000 -40,000 -75,000 685,000

Failure Electronic (cost) -40,000 Patent (cost) -75,000 -115,000 Total

EV = 0.75 (685,000) + 0.25 (-115,000) = 513, 750 – 28,750 = 485,000

Position B: Options/Alternatives Electronic system = ₱385,000 Manual system = ₱485,000 Thus, best alternative is manual system.

Position A: Final Alternatives Purchase patent = ₱485,000 Not = 0

The options indicated in position B are ₱385,000 and ₱485,000 for the best system. And in position A, final alternatives are ₱485,000 and 0. Decision: The company should purchase the patent and expect a larger profit in choosing the best system as an alternative which is the manual system since after deducting the given costs it would result to higher amount of income that electronic system.

Problem_3

Method A Cost: -₱120,000

D

Success

8,000,000 -120,000 - 12,000

P=0.8 Failure P=0.2

A

Submit proposal Cost: -₱12,000

Not

0

Receive contract

B

Method B

C

P=0.5

Not receive

(0) -₱12,000

P=0.5

Cost: -₱50,000

Method C Cost: -₱30,000

F

(0) -120,000 - 12,000

Success

E

8,000,000 -50,000 - 12,000 Failure (0) P=0.4 -50,000 - 12,000

P=0.6

Success P = 0.45

8,000,000 -30,000 - 12,000

Failure P = 0.55 Method A Cost: -₱120,000

6,268,000

Success P=0.8

7,868,000

Failure P=0.2 Prepare proposal

A

Submit proposal 3,128,000

Cost: -₱12,000

6,268,000

Method B

0 -30,000 - 12,000

4,738,000

-132,000

Success 7,938,000

Cost: -₱50,000

P=0.5

P=0.6

Not

0

Failure Not P=0.5

(0) -₱12,000

P=0.4 Method C Cost: - ₱30,000

3,558,000

Success P = 0.45

7,958,000

Failure P = 0.55

-42,000

-62,000

Solutions: Position D: Method A Position F: Method C Success Success 8,000,000 Cost: Method A -120,000 Cost: Proposal -12,000 Total 7,868,000

Failure Cost: Method A -120,000 Cost: Proposal -12,000 Total -132,000

EV = 0.8 (7,868,000) + 0.2 (-132,000) = 6,294,400 – 26,400 = 6,268,000 Position E: Method B Success Success 8,000,000 Cost: Method B -50,000 Cost: Proposal -12,000 Total 7,938,000

Failure Cost: Method A -50,000 Cost: Proposal -12,000 Total -62,000

Success Success 8,000,000 Cost: Method C -30,000 Cost: Proposal -12,000 Total 7,958,000 Failure Cost: Method A -30,000 Cost: Proposal -12,000 Total -42,000 EV = 0.45 (7,958,000) + 0.55 (-42,000) = 3,581,100 – 23,100 = 3,558,000

EV = 0.6 (7,938,000) + 0.4 (-62,000) = 4,762,800 – 24,800 = 4,738,000 Position C: Options/Alternatives

Position B:

Method A = ₱6,268,000 Method B = ₱4,738,000 Method C = ₱3,558,000

EV = 0.5 (6,268,000) + 0.5 (-12,000)

Position A: Final Alternatives Prepare proposal = ₱3,128,000 Not = 0

= 3,134,000 – 6,000 = 3,128,000

Thus, the final alternative is method A. The options enumerated (methods) for position C are ₱6,268,000, 4,738,000 and ₱3,558,000. Moreover, ₱3,128,000 and 0 at position A are the final alternatives. Decision:

ILY construction should prepare the proposal for developing a ne w product since it is expected to result a proft of ₱ 3,128,000.

Problem_4

Method A

Success

D

Cost: -₱120,000

8,000,000 -120,000 - 12,000

P=0.8 Failure P=0.2

Prepare proposal

A

Submit proposal

C

B Cost: -₱12,000 Not 0

Method B

-100,000 -120,000 - 12,000

Success

E P=0.6

Cost: -₱50,000

P=0.5

8,000,000 -50,000 - 12,000 Failure

-100,000 -50,000 - 12,000

Not (0)

P=0.5

– 12,000

P=0.4 Method C

F

Cost: -₱30,000

Success P = 0.45

8,000,000 -30,000 - 12,000

Failure

-100,000 -30,000 - 12,000

P = 0.55 Method A 6,248,000 Success

Cost: -₱120,000

7,868,000

P=0.8

Failure P=0.2 Prepare proposal

A

Submit proposal 3,118,000 P=0.5

Cost: -₱12,000

Not

0

6,248,000

Method B

4,698,000

Success

Not P=0.5

7,938,000

P=0.6 Failure

Cost: -₱50,000

(0) – 12,000

-232,000

P=0.4 Method C Cost: -₱30,000 3,503,000

Success P = 0.45

7,958,000

Failure P = 0.55

-142,000

-162,000

Solutions: Position D: Method A

Position C: Options/Alternatives

Success

Failure

8,000,000 -120,000 -12,000 7,868,000

Success Cost: Method A Cost: Proposal Total

Failure Cost: Method A Cost: Proposal Total

-100,000 -120,000 -12,000 -232,000

Method A = ₱6,248,000 Method B = ₱4,698,000 Method C = ₱3,503,000 Thus, the final alternative is method A.

EV = 0.8 (7,868,000) + 0.2 (-232,000) = 6,294,400 – 46,400 = 6,248,000 Position E: Method B

Position B:

Success Success 8,000,000 Cost: Method B -50,000 Cost: Proposal -12,000 Total 7,938,000

Failure Failure Cost: Method A Cost: Proposal Total

-100,000 -50,000 -12,000 -162,000

EV = 0.6 (7,938,000) + 0.4 (-162,000) = 4,762,800 – 64,800 = 4,698,000 Position F: Method C Success Success Cost: Method C Cost: Proposal Total EV

Failure 8,000,000 -30,000 -12,000 7,958,000

Failure Cost: Method A Cost: Proposal Total

-100,000 -30,000 -12,000 -142,000

EV = 0.5 (6,248,000) + 0.5 (-12,000) = 3,124,000 – 6,000 = 3,118,000

Position A: Final Alternatives Prepare proposal = ₱3,118,000 Not = 0

= 0.45 (7,958,000) + 0.55 (-142,000) = 3,581,100 – 78,100 = 3,503,000 The options in position C are ₱6,248,000, 4,698,000 and ₱3,503,000. And the final alternatives are ₱3,118,000 and 0 at position A. Decision: It is a must for ILY construction to prepare and submit a proposal in spite of the penalty if the company fails to develop the product, because it is still expected to gain a profit amounting ₱3,118,000.

Problem_5

Customer testing

A

B

Not

Favorable P = 0.60

C

Cost: -₱50,000

Make a new face powder

Unfavorable

E

-500,000 -50,000

P = 0.40 0

Without testing

D

Success P = 0.60 Failure P = 0.40

Customer testing Make a new face powder

A

Cost: -₱50,000

400,000 Not

125,000

Success 400,000 P = 0.60 Failure P = 0.40

Failure

1,000,000 -50,000 -500,000 -50,000

1,000,000

-500,000

575,000

-550,000

0 Without testing

P = 0.75

P = 0.25

Favorable P = 0.60

Unfavorable P = 0.40

Success

1,000,000 -500,000

Success P = 0.75 Failure P = 0.25

950,000 -550,000

Solutions: Position E: Success Success Cost: customer testing Total EV

1,000,000 -50,000 950,000

Failure Failure Cost: customer testing Total

-500,000 -50,000 -550,000

= 0.75 (950,000) + 0.25 (-550,000) = 712,500 – 137,500 = 575,000

Position C : Customer testing EV

= 0.60 (575,000) + 0.40 (-500,000 -50,000) = 345,000 – 220,000 = 125,000

Position D: Without testing EV = 0.60 (1,000,000) + 0.40 (-500,000) = 600,000 – 200,000 = 400,000 Position B: Options/Alternatives Customer testing = ₱125,000 Without testing = ₱400,000 Position A: Final Alternatives Make a new face powder = ₱400,000 Not = 0

The options in position B are ₱125,000 and ₱400,000 and the final alternatives in position A are ₱400,000 and 0. Decision: Avon cosmetics should push the approach to make a new face powder without customer testing since it would result to a higher amount of income than having a testing program. Gaining a proft of ₱ 400,000 is so much beter than expecting nothing at all.

Problem_6 Report for work

Get sick

B

-200

P = 0.40

A

Not get sick 0

P = 0.60 Stay home and rest -120 Report for work Get sick

-80

-200

P = 0.40 Not get sick

A

0

P = 0.60 Stay home and rest -120 Solution: Position A: Final Alternatives

Position B: EV = 0.40 (-200) + 0.60 (0) = -80 + 0 = -80

Report for work = -₱80 Stay home and rest = ₱120

The final alternatives are -80 and -120. Decision: Myra should report for work instead of staying home to save more money. In this case, it would be practical for her to acquire an expense of ₱80 than a deduction from her salary costing ₱120 for her absence.

Problem_7

Success 660,000

Colgate Cooling Crystals

P = 0.35

B

Failure -220,000 P = 0.65

A

Success

Colgate with fluoride

C

220,000 P = 0.35 Failure -88,000

Do nothing

P = 0.65

0

Success 660,000

P = 0.35 Colgate Cooling Crystals

88,000

Failure -220,000

P = 0.65 Success

A

19,800 Colgate with fluoride

220,000

P = 0.35 Failure P = 0.65

0 Do nothing

-88,000

Solutions:

Position B: EV = 0.35 (660,000) + 0.65 (-220,000) = 231,000 – 143,000 = 88,000

Position C: EV = 0.35 (220,000) + 0.4 (-88,000) = 77,000 – 57,200 = 19,800

Position A: Final Alternatives Colgate Cooling Crystals = ₱88,000 Colgate with fluoride = ₱19,800 Do nothing = 0

The final alternatives are ₱88,000, ₱19,800 and 0. Decision: The market analyst of Colgate should launch a new product. In particular, he should launch Colgate with cooling crystals and expect a profit of ₱88,000.

Problem_8

Resign (Apply for a job)

Success

B

A Not resign

34,000 P = 0.80 Failure

17,000

0

P = 0.20

Resign (Apply for a job)

Success 27,200

A Not resign

34,000 P = 0.80 Failure

17,000

0

P = 0.20

Solution: Position B: EV

= 0.80 (34,000) + 0.20 (0) = 27,200 + 0 = 27,200

Position A: Final Alternatives Resign = ₱27,200 Not resign = ₱17,000

The final alternatives are ₱27,200 and ₱17,000. Decision: Mighty should resign from his post and apply for a job since the expected value of this alternative is much higher than choosing not to resign – (27,200 > 17,000)....