Question $3(25$ marks$)$

Barloworld Botswana Ltd manufactures automobiles in two plants based in Okavango Delta namely,

$O_1$ and $O_2$ and then ships them to three cities around the country namely $D_1,D_2$ and $D_3.$ The supply and

demand amounts and corresponding shipping costs are shown in the network below. Barloworld

Botswana Ltd wants to find the lowest$-$cost distribution plan for meeting the demands of the three

cities without exceeding the capacities of the plants.

Develop and optimize the problem for Barloworld using northwest corner method to help achieve the

least$-$cost way of distributing her automobiles from Okavango plants to demand cities. In your

modelling, clearly, show:

a$)$ A complete transport tableau.

$(6$ marks$)$

b$)$ The variables in the model. $(2$ marks$)$

c$)$ Relevant linear constraints. $(7$ marks$)$

d$)$ The solution and its interpretation. $(10$ marks$)$