Operations Research/Management Science Study

1. Case Analysis:
The Condominium

2. Scenario
Dave is a businessman whose business is buying repossessed
condominiums from lending institutions and banks. Dave was offered by
the Blue Key Savings and Loan associations three units that he must all
take at a non-negotiable price of $ 72,000.00. If Dave will buy the units, he
is given 60 days by the savings and loan associations to pay the
purchased amount $ 72,000.00. Dave believes that he has 70% chance of
selling the units within the allotted 60 days. However, any unit which was
not sold within 60 days would be sold, for certainty. Within 30 days but in
that case there would be a financial charge for late payment of $440 per
apartment. What must Dave’s decision should be?
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3. Things To Consider
Given Dave’s situation, he must consider the following:
1. If he purchased and sold all the units, how much is the
maximum profit that he can earn?
2. If he can sell all the units within 60 days, how much is
his profit?
3. If he sells the units after 60 days, how much would he
earn?

4. Decision Alternatives:
1. Decline the offer
2. Buy the units
 To sell the units at low prices
 To sell the units at moderate prices
 To sell the units at high prices
States of Nature:
If Dave would buy the units the following are the state of natures:
 State of nature 1: Dave would be able to sell the units
within 60 days (0.70)
 State of nature 2: Dave could sell the units after 60 days
or within 90 days. (0.30)
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Things To Consider

5. Solution
Compute for the payoff for each apartment unit:
Expected Revenue from Each Unit
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Selling
Price
Advertising,
Legal, Finance
etc
Sales(60 Days) Financial
Charge
Sales(90 Days)
Decline $0.00 $0.00 $0.00 $0.00 $0.00
Purchase All:
Unit 1 $26,900.00 ($1,000.00) $25,900.00 ($440.00) $25,460.00
Unit 2:
25% $25,000.00 ($1,000.00) $24,000.00 ($440.00) $23,560.00
50% $26,000.00 ($1,000.00) $25,000.00 ($440.00) $24,560.00
25% $27,000.00 ($1,000.00) $26,000.00 ($440.00) $25,560.00
Unit 3:
30% $25,000.00 ($1,000.00) $24,000.00 ($440.00) $23,560.00
40% $26,000.00 ($1,000.00) $25,000.00 ($440.00) $24,560.00
30% $27,000.00 ($1,000.00) $26,000.00 ($440.00) $25,560.00

6. Decisions
State of Nature
Higher Chance of
Selling the Units
Within 60 days
(70%)
Lower Chance of
Selling the Units
Within 90 days
(30%)
Purchase:
Unit 1 $25,900.00 $25,460.00
Unit 2:
25% $24,000.00 $23,560.00
50% $25,000.00 $24,560.00
25% $26,000.00 $25,560.00
Unit 3
30% $24,000.00 $23,560.00
40% $25,000.00 $24,560.00
30% $26,000.00 $25,560.00
Solution

7. Construct a payoff table
 Sold low = 25,900+24,000+24,000 =73,900
 Sold Moderate = 25,900+25,000+25,000 = 75,900
 Sold high = 25,900+26,000+26,000=77,900
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Selling the
Units Within
60 days
(70%)
Selling the
Units Within 90
days
(30%)
1.Sold Low $73,900.00 $72,580.00
2.Sold Moderate $75,900.00 $74,580.00
3.Sold High $77,900.00 $76,580.00
Payoff Table
Solution

8. 8
Payoff Table
 If Dave will sell the units at high prices within 60 days, he can
have a profit $5,900.00 ($77,900 - $72,000).
Solution
Selling the
Units Within
60 days
(70%)
Selling the
Units Within 90
days
(30%)
1.Sold Low $73,900.00 $72,580.00
2.Sold Moderate $75,900.00 $74,580.00
3.Sold High $77,900.00 $76,580.00

9. Decisions
State of Nature
Expected
Payoff
Selling the
Units W/n 60
days
(70%)
Selling the
Units W/n 90
days
(30%)
Purchase:
1.Sold Low $73,900.00 $72,580.00 $ 73,504
2.Sold Moderate $75,900.00 $74,580.00 $ 75,504
3.Sold High $77,900.00 $76,580.00 $ 77,504
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Compute for Expected Payoff
EP1= (73,900*.7) + (72,580*.3) = $ 73,504
EP2 = (75,900*.7) + (74,580*.3) = $ 75,504
EP3 = (77,900*.7) + (76,580*.3) = $ 77,504
Solution

10. Compute the Profit under each alternative:
The following will be the profits of Dave for each alternative:
• EP1 = 73,504 - 72000 = $1,504
• EP2 = 75,504 – 72,000 = $3,504
• EP3 = 77,504 – 72,000 = $5,504
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Solution
Decisions
State of Nature
Expected
Payoff
Selling the
Units W/n 60
days
(70%)
Selling the
Units W/n 90
days
(30%)
Purchase:
1.Sold Low $73,900.00 $72,580.00 $ 73,504
2.Sold Moderate $75,900.00 $74,580.00 $ 75,504
3.Sold High $77,900.00 $76,580.00 $ 77,504

11. 11
Expected Opportunity Loss (EOL) Table
Compute the expected opportunity loss
EOL1 = (4,000*.7) + (4,000*.3) = $4,000
EOL2 = (2,000*.7) + (2,000*.3) = $2,000
EOL3 = (-) + (-) = $0
Decisions
State of Nature
Expected
Opportunity
Loss
Selling the
Units
Within 60
days
(70%)
Selling the Units
Within 90 days
(30%)
Purchase:
1.Sold Low $4,000.00 $4,000.00 $4,000
2.Sold Moderate $2,000.00 $2,000.00 $2,000
3.Sold High $0.00 $0.00 $0
Solution

12. As seen in the decision tables, we recommend to Dave
that:
• He must buy the units since he has a greater chance to
sell it within 60 days and earn profits.
• Whether he sells it within 60 or 90 days, he still can
earn profits.
• Selling the units in the highest possible price can
maximize his profits.
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Advise