Consider the following three securities:

Security A is a 2-year zero, which matures two years from today, and pays $1 at maturity.

Security B is a 3-year zero, which matures three years from today, and pays $1 at maturity.

Security C is a 1-year forward contract, which matures one year from today, and delivers a 1-year zero (with face value $1) at maturity.

My portfolio currently consists of a long position of 5,000 units of security B and a short position (liability) of 3,000 units of security A. Suppose the only securities I can currently trade (buy/sell) are Security A and Security C. The current term structure based on zero coupon bonds *with1, 2-, 3-, and 4-year maturity from today) in annualized rates with continuous compounding is:

r₁ = 5% r₂ = 6% r₃ = 8% r₄ = 10%

Without changing the value of my portfolio (found in part (a), what do I have to do now (i.e. if anything, long/short what? How much?) to achieve a dollar duration of zero for my portfolio? (Suppose I dont care about convexity.)