A financial institution has the following portfolio of over-the-counter options on sterling:

Type	Position	Delta of Option	Gamma of Option	Vega of Option
Call	?1,000	0.5	2.2	1.8
Call	?500	0.8	0.6	0.2
Put	?2,000	-0.40	1.3	0.7
Call	?500	0.70	1.8	1.4

A traded option (different from the options in the portfolio) is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8 (8 points in total).

What position in the traded option and in sterling (the underlying asset) would make the portfolio both gamma neutral and delta neutral? (Hint: you need to calculate the delta and gamma of the portfolio before you add in the new option and the underlying asset. Then you can try to make the new portfolio (after you add in the new option and the underlying asset) gamma and delta neutral) (4 points)

What position in the traded option and in sterling would make the portfolio both vega neutral and delta neutral? (4 points)