Chapter 8.5, Problem 3E

Repeat Exercise 1 where m is the minimum value of f on S instead of the maximum value.

1. Given points p₁ = $\left[\begin{array}{c}1\\ 0\end{array}\right]$, p₂ = $\left[\begin{array}{c}2\\ 3\end{array}\right]$, and p₃ = $\left[\begin{array}{c}-1\\ 2\end{array}\right]$ in ℝ², let S = conv {p₁, p₂, p₃}. For each linear functional f, find the maximum value m of f on the set S, and find all points x in S at which f(x) = m.

1. a. f(x₁, x₂) = x₁ − x₂
2. b. f(x₁, x₂) = x₁ + x₂
3. c. f(x₁, x₂) = −3x₁ + x₂