We return to the coal mining example, which is Example 4 of Chapter 2, Section 3.

(a) Identify the vectors \(\mathbf{b}^{*}\) and \(\mathbf{c}^{*}\) and the matrix \(S\) of Figure 3.5 for this problem.

(b) Express the problem in the form of formula (4).

(c) Verify the equations in parts (b) and (c) of Theorem 1 for this problem.