Your company has three production plants $($Plant A$,$ Plant B$,$ and Plant C$)$ and four distribution centres $($Centre $1,$ Centre $2,$ Centre $3,$ and Centre $4).$ The production capacity and demand for each product at the plants and centres are as follows:

Production Capacity at Plants:

Plant A: $300$ units of Product X$,200$ units of Product Y

Plant B: $400$ units of Product X$,300$ units of Product Y

Plant C: $500$ units of Product X$,100$ units of Product Y

Market Demand at Distribution Centers:

Center $1$: $200$ units of Product X$,300$ units of Product Y

Center $2$: $400$ units of Product X$,100$ units of Product Y

Center $3$: $300$ units of Product X$,100$ units of Product Y

Center $4$: $300$ units of Product X$,100$ units of Product Y

Transportation Costs $($in RM$)$ per unit from Plants to Centers:

Center $1$ Center $2$ Center $3$ Center $4$

Plant A $5748$

Plant B $8965$

Plant C $10687$

Objective:

Minimise the total transportation cost while meeting the demand and production constraints.