Question $2[10$ points$]$

PEE PTE LTD is an Asia$-$based personal edutainment electronics manufacturer that

produces a highly successful edutainment product, P$-$WEE$-8.$ It has four plants that

manufacture the product and three regional distribution centres. To improve its cost

competitiveness, the company is considering reducing its fixed operating and production

costs by closing one or more plants, even though it would incur an increase in

transportation costs. The relevant data on costs, annual production capacities and annual

demands for the problem are provided in the following table. Annual fixed operating costs

need to be incurred only if a plant is open.

In the provided table, consider the following scenario: if Plant $1$ is open, it will face fixed operating costs

of $$900,000.$ The manufacturer determines the production quantity in Plant $1,$ ensuring it does not exceed

the production capacity, with a production cost per unit of $$120.$ Subsequently, following the production

process, all products are dispatched from Plant $1$ to various centers $($Center $A,B,C)$ with varying

shipping costs to fulfill demands.

Hint: the total production quantity in a plant $=$ the total amount of products shipped from that plant to all

centers.

Formulate a mixed integer programming model of this problem to assist the company in determining $(1)$

which plants should remain open and which should be closed and $(2)$ the number of units that should be

shipped from each plant to each distribution centre, in order to minimize total cost. $($Write down explicitly

the objective function and all functional constraints in terms of the decision variables$).$ State the optimal

solution by solving this problem with Excel Solver.