Grade 4: OR Section Term 2 Section 5 Linear Programming applications (2) Youtube: https://youtu.be/EyeY9p8jooE

1. By:
Zakaria Elsayed Hasaneen
Teaching Assistant at Faculty of Commerce
Accounting Department (English Section)
Kafrelsheikh University
OR
Section (5)
Linear Progamming applications (2)
Grade 4 –Term 2
Zakaria Hasaneen
Zakaria Hasaneen
Zakaria Hasaneen

2. Portfolio selection Problem
ZAK Trust must decide how to invest $8 million .
Investment Projected Return Risk Factor
Petroleum 14% 5
Stocks 16.5% 7
Gold 10% 2
Real Estate 12% 3

3. Required :
How much should ZAK invest in these alternatives to maximize dollar return on
investment?
A. No single investment alternative should account for more than 40% of
budget.
B. A mount invested in Gold and Real Estate combined must be at least twice
that invested in in Petroleum
C. The risk associated with Stocks should not exceed twice the risk associated
with Real Estate .
D. Investment in real estate should exceed investment in Stocks by no more
than $1 Million.
E. Average risk factor should be no more than 5.
Guidelines:

4. Decision
variables

5. Objective Function

6. ZAK Trust must decide how to invest $8 million .

7. A.No single investment alternative should account for
more than 40% of budget.

9. B- A mount invested in Gold and Real Estate combined
must be at least twice that invested in Petroleum

10. C- The risk associated with Stocks should not exceed
twice the risk associated with Real Estate .

11. D-Investment in real estate should exceed investment
in Stocks by no more than $1 Million.

12. E-Average risk factor should be no more than 5.

13. Non-negativity constraints

14. Transportation Problem
LP Formulation