The costs $($in rand$)$ of shipping units from two plants to three warehouses are shown in Table $2.$

$\backslash$table$[[\backslash$table$[[$From$],[$plant$]],$To warehouse$],[1,2,3],[1,1,3,1,9,1,8],[2,1,7,1,2,1,4]]$

Table $2$: Shipping cost per unit $($in rand$)$

$4.$ If $f$ is continuous on the interval $a$;$b$ and there is a function $F$ such that $F^{\text{'}}(x)=f(x),$ then

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx=F(b)-F(a)$

This is called the fundamental theorem of integral calculus.

$5.$ Generalising from this structure, Gupta proposed that for $m>2$ the job index to be calculated is

$s_j=\frac{e_j}{mi{n}_1}km-1\{t_{jk}+t_{j(k+1)}\}$

with

$e_j=\{\begin{array}{ccc}1& if& t_{j1}=t_{jm}\end{array}$

$15$