Q $3($b$)[15$ Marks$]$

A shoe company forecasts the following demands during the next three months: $200,$

$260,240.$ It costs $7$ to produce a pair of shoes with regular time labour $($RT$)$ and

$11$ with overtime labour $($OT$).$ During each month regular production is limited to

$200$ pairs of shoes, and overtime production is limited to $100$ pairs. It costs $1$ per

month to hold a pair of shoes in inventory. Customers are willing to wait a maximum

of one month for their order to be fulfilled at a cost of $4$ per pair of shoes.

$1.$ Formulate a balanced transportation problem to minimize the total cost of

meeting the next three months of demand on time. $(2$ Marks$)$

$2.$ Apply the North$-$West Corner Rule to determine an initial feasible solution.

$(5$ Marks$)$

$3.$ Apply an iteration of the Modi Method and comment on the cost of this

solution in comparison to the cost of the initial feasible solution. $(8$ Marks$)$