6. (10 points) Suppose a Delta-neutral portfolio contains option A, option B, and underlying asset. The Gamma and Vega of this portfolio are 1,500 and 1,000, respectively. Option A has a Delta of 0.4, Gamma of 1.0 and Vega of 1.5. Option B has a Delta of 0.5, Gamma of 1.5 and Vega of 0.5. The new portfolio will be both Gamma-neutral and Vega-neutral when adding wa of option A and wo of option B into the original portfolio. a) Please determine the value of wa and wb. b) Calculate the Delta of the new portfolio. c) Determine the number of shares we need to short to maintain the portfolio Delta-neutral