Question $1(30$ marks$)$

Shops Limited has warehouses in three locations and is currently operating three shops

situated in different locations from the warehouses. The transport cost per consignment of

goods, the capacity of the warehouses and the shops requirements are as follows:

From To Shop A Shop B Shop C Capacity

Location $1$ N$$100$ N$$40$ N$$11070$

Location $2$ N$$120$ N$$50$ N$$8050$

Location $3$ N$$90$ N$$70$ N$$6030$

Demand $405060150$

Required

Marks

Sub$-$

total Total

$1\mathrm{.}1$ Find the initial solution by applying the north$-$west corner method. $66$

$1\mathrm{.}2$

Use the modified distribution $($MODI$)$ method to determine whether

the solution provided in $(1\mathrm{.}1)$ above, results in the optimal minimum

transportation costs.

$1420$

$1\mathrm{.}3$

Assuming the company want to change the method of determining

the initial solution, use the Vogel approximation method to find the

initial solution.

$1030$