Prove that there exists a unique efficient alternative in s

Question

Let (S, d) ∈ F be a bargaining game.

(a) Prove that there exists a unique efficient alternative in S minimizing the absolute value |(x₁ - d₁) - (x₂ - d₂)|. Denote this alternative by x∗.

Let Y be the collection of efficient alternatives y in S satisfying the property that the sum of their coordinates y₁ + y₂ is maximal.

(b) Show that the Nash solution N (S, d) is on the efficient boundary between x∗ and the point in Y that is closest to x. In particular, if x∗ ∈ Y then x^∗ = N (S, d).