helpA delivery rider wants to deliver food stock from four markets to four restaurants. The food supply from the markets, the restaurants demand for each stock and the cost associated with a unit delivery service are summarized in Table $2.$

Table $2$

$\backslash$table$[[,$Destination $($Restaurants$),,],[$D$1,$D$2,$D$3,$D$4,$Supply,$],[$Source $($Markets$),$S$1,5,1,8,7,15],[$S$2,3,9,6,7,25],[$S$3,4,2,7,6,42],[,$S$4,7,11,10,4,35],[,$Demand,$30,20,15,30,]]$

$($a$)$ Add either a dummy row or a dummy column for the transportation problem above to be balanced, i$.$e$.,$ Demand $=$ Supply $.$

$[2$ Marks$]$

$[$CO$1,$ PO$1,$ C$3]$

$($b$)$ Find the starting basic solution for the transportation problem in $($a$)$ using

i$)$ Northwest Corner Method

$[3$ Marks$]$

$[CO1,PO1,C3]$

ii$)$ Vogel Approximation Method

$[3$ Marks$]$

$[$CO$1,$ PO$1,$ C$3]$

$($c$)$ Based on the result from $($b$),$ use the worst starting basic solution and improve the solution by one iteration using the multiplier method.

$[12$ Marks$]$

$[$CO$2,$ PO$2,$ C$4]$

$4$