An investor has liabilities of $2m and $3m due at times t = 4 and 5, respectively. He currently holds assets X and Y. If each unit of X produces an income of $1m at t = 4 and each unit of Y produces $1m at t = 8, construct a portfolio consisting of the liabilities and amounts of X and Y that is immune to small changes in interest rate at i = 5% per annum.