QUESTION $2$: $($CLO $4-10$ Marks$)$

The distribution system for the Sahara Company consists of three plants, two warehouses $($hub$),$ and four customers. Plant capacities and shipping costs per unit $($in AED$)$ from each plant to each warehouse are as follows:

PLANT WAREHOUSES

$12$ CAPACITY

$136500$

$274650$

$347450$

Customer demand and shipping costs per unit $($in Dirhams$)$ from each warehouse to each customer are:

$1$

WAREHOUSE CUSTOMER

$1234$

$17546$

$24653$

DEMAND $450300400500$

$($a$)$ Develop a network representation of this problem. $(3$ Marks$)$Now suppose that shipments between warehouse $1$ and warehouse $2$ are permitted $($both ways$)$ at $5$ Dirhams per unit and that direct shipments can be made from plant $3$ to customer $4$ at a cost of $7$ Dirhams per unit.

$($b$)$ FORMULATE a linear programming model of the problem

$($c$)$ DEVELOP a network representation of this problem. $(2$ Marks$)$

$[$You don$$t have to draw a new network representation $-$ You can just make additions to the network drawn in $($a$)$ above if possible using a different ink$].$

$($d$)$ Now re$-$formulate a linear programming model for the problem with the added information $($if possible show the added information in a different ink$).$