$($Carlos F$.$ Daganzo: Logistics Systems Analysis, $4$th Ed$.$ Springer, $2004)$ Create a numerical example to show the effectiveness of the solution approach for

solving the unconstrained minimum of $(4\mathrm{.}20$a$).$ Assess the error by computing the

relative error. $($hint: the "true" solution can be obtained by enumeration using

MATLAB or other computer programs$).$

$z={}_0+{}_1([1],[n_{s}v])+{}_2([l],[v])+{}_3(n_s)+{}_4(v)$

${}_0=(c_s+c_i\frac{r}{s}+c_i\frac{l_s}{2})$; handling and lixed pipeline inventory cost per

item,

${}_1-(2r{c}_d+c_s)$; transportation cost per dispatch,

${}_2-(c_{d}k{}^{-\frac{1}{2}}+c_s)$; transportation cost added by a customer detour,

${}_3=\frac{1}{2}{c}_i(k\frac{{}^{-\frac{1}{2}}}{s}+1_s)$; pipeline inventory cost per item caused by a

customer detour and the ensuing stop,

${}_4-c_h{D}^{\text{'}}$; stationary holding cost of holding one item during the time

$(1/$D$\text{'})$ between demands.