__4.__ The deterministic (no randomness) problem $$ \min C(x) = c_u (D - x)^+ + c_o (x-D)^+ \qquad\qquad\qquad (1) $$is trivial and has a trivial solution -- namely, $x_{\ast} = D$. However, it still has value because it has a _dual_. Show that the linear program for (1) is given by$$\begin{eqnarray*} \min & c_u \mu + c_o u \\ s.t. \;\; & x+\mu \ge D \\ & x-u \le D \\ & x \ge 0, \mu \ge 0, u \ge 0 \end{eqnarray*}$$Then find the dual and the shadow price for the primal model (1).