please help for this math and finance problem, thanj you

2. A financial institution has the following portfolio of over-the-counter options on ster- ling: Delta of Type Position Each Option Call -1000 0.5 Call -500 0.8 Put -2000 -0.4 Call -500 0.7 Gamma of Vega of Each Option Each Option 2.2 1.8 0.6 0.2 1.3 0.7 1.8 1.4 A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8. (a) What position in the traded option and in sterling would make the portfolio both gamma-neutral and delta-neutral? (b) What position in the traded option and in sterling would make the portfolio both vega-neutral and delta-neutral