The ABC Company has two manufacturing plants on opposite sides of India. Each of these plants

produces the same two products and then sels them to wholesalers within its half of the country. The

orders from wholesalers have already been received for the next $2$ months $($February and March$),$ where

the number of units requested are shown below $($The compary is not abligated to completely fill these

orders but will do sa if it can without decreasing its profits$).$

Each plant has $20$ production days available in February and $23$ production days available in March to

produce and ship these products. Inventories are depleted at the end of January, but each plant has

enough inventary capacity to hold bath the two products if an encess amount is produced in February for

sale in March. In either plant, the cost of halding imentory in this way is $$3$ per unit of product $1$ and $$4$

per unit of Praduct $2.$

Each plant has the same two production processes, each of which can be used to produce either of the

two praducts. The production cast per unit produced of each praduct is shown below for each process in

each plant.

Name:

Roll No

The production rate far each product $($number of units produced per day devoted to that product$)$ also is

given for each process in each plant.

The net sales revenue $($selling price minus normal shipping costs$)$ the compary receives when a plant sells

the products to its own custamers $($to wholesalers in its half of the country$)$ is $$83$ per unit af Product $1$

and $$112$ per unit of Product $2.$ However, it is also possible $($and occasionally desirable$)$ for a plant to make

a shipment to the other half of the country to help fill the sales of the other plant. When this happens, an

eatra shipping cost of $$9$ per unit af praduct $1$ and $$7$ per unit of Praduct $2$ is incurred.

The manager Mr$.$ Ances P M$,$ who happens to be an IIMX graduate and also the Chief Technology

officer, needs to determine how much of each product shauld be produced by each production process

in each plant during each month, as well as haw much each plant should sell each product in each manth

and how much each plant should ship of each product in each month to the other plant's customers. The

objective is to determine the optimal plan that wauld maximize the total prafit $($tatal net sales revenue

minus the sum of the production costs, inventory costs, and extra shipping costs$).$ Formulate this

aggregate production planning problem as a transportation problem $($Transportation table is NECESSARY

and SUFFICIENT$]$