Title: Solving a Transportation Model Problem

Background:

Your company is a leading bycycle manufacturing company with multiple production plants and distribution centres across Malaysia. They produce various parts and assemble finished bicycles. Your company aims to maximise its profit by determining the optimal production and distribution plan while adhering to constraints such as production capacities, resource availability, and market demand.

Problem Description:

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.