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3. A hedge fund has two trading desks (A and B ) which have different traders with different trading strategies. The hedge fund has up to $10 million in total which it can allocate to the two desks for them to start investing. However, it can only allocate at most $7 million to each desk to follow the diversification information given to investors. After 1 year, it is expected that desk A will make a 5% return (i.e. for every $1 in initial funding it will end with $1.05 for a profit of $0.05) and desk B will make a 10% return. However, for every $1 million in initial funding, desk A requires 3 support staff (for trade execution, risk management, IT, etc) and desk B requires 5 support staff. There are only 40 support staff available. (a) Formulate an LP problem to determine how the fund should best allocate its initial funding to maximise the profit in the first year. (b) Solve the hedge fund's problem using the simplex method.

3. A hedge fund has two trading desks (A and B ) which have different traders with different trading strategies. The hedge fund has up to $10 million in total which it can allocate to the two desks for them to start investing. However, it can only allocate at most $7 million to each desk to follow the diversification information given to investors. After 1 year, it is expected that desk A will make a 5% return (i.e. for every $1 in initial funding it will end with $1.05 for a profit of $0.05) and desk B will make a 10% return. However, for every $1 million in initial funding, desk A requires 3 support staff (for trade execution, risk management, IT, etc) and desk B requires 5 support staff. There are only 40 support staff available. (a) Formulate an LP problem to determine how the fund should best allocate its initial funding to maximise the profit in the first year. (b) Solve the hedge fund's problem using the simplex method.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. A hedge fund has two trading desks (A and B ) which have different traders with different trading strategies. The hedge fund has up to $10 million in total which it can allocate to the two desks for them to start investing. However, it can only allocate at most $7 million to each desk to follow the diversification information given to investors. After 1 year, it is expected that desk A will make a 5% return (i.e. for every $1 in initial funding it will end with $1.05 for a profit of $0.05) and desk B will make a 10% return. However, for every $1 million in initial funding, desk A requires 3 support staff (for trade execution, risk management, IT, etc) and desk B requires 5 support staff. There are only 40 support staff available. (a) Formulate an LP problem to determine how the fund should best allocate its initial funding to maximise the profit in the first year. (b) Solve the hedge fund's problem using the simplex method. (c) By considering the optimum of the dual problem, identify which constraint (s) would have the largest relative impact on the optimal profit if it could be relaxed (i.e. the corresponding resource value increased).
Transcribed Image Text:3. A hedge fund has two trading desks (A and B ) which have different traders with different trading strategies. The hedge fund has up to $10 million in total which it can allocate to the two desks for them to start investing. However, it can only allocate at most $7 million to each desk to follow the diversification information given to investors. After 1 year, it is expected that desk A will make a 5% return (i.e. for every $1 in initial funding it will end with $1.05 for a profit of $0.05) and desk B will make a 10% return. However, for every $1 million in initial funding, desk A requires 3 support staff (for trade execution, risk management, IT, etc) and desk B requires 5 support staff. There are only 40 support staff available. (a) Formulate an LP problem to determine how the fund should best allocate its initial funding to maximise the profit in the first year. (b) Solve the hedge fund's problem using the simplex method. (c) By considering the optimum of the dual problem, identify which constraint (s) would have the largest relative impact on the optimal profit if it could be relaxed (i.e. the corresponding resource value increased).
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