On August 1 a portfolio manager has a bond portfolio worth $10 million. The duration of the portfolio in October will be 7.1 years. The December Treasury bond futures price is currently 91-12 and the cheapest-to-deliver bond will have a duration of 8.8 years at maturity.

a) How should the portfolio manager immunize the portfolio against changes in interest rates over the next two months?

b) How can the portfolio manager change the duration of the portfolio to 3.0 years?

(Please do calculations)