The Standard Cars Limited currently has four plants for manufacturing and assembling cars and six warehouses where these are transported for subsequent delivery to its dealers/showrooms. The company management has collected the following information:

Annual production capacity of each plant, Annual demand of cars at various warehouses, Costs involved in transporting cars from various plants to different warehouses, and Annual fixed operating costs for each of the plants.

The information is summarised in the following table:

To illustrate, plant 3 has a total annual capacity of 48 thousand cars; the demand at warehouse 2 is 12,000 cars per annum; the cost of transporting 1,000 cars from plant 3 to warehouse 5 is Rs 32,000; and plant 4 has an annual fixed operating cost equal to Rs 168,000. Currently, the company is sending the cars as per the following schedule:

This schedule involves a total cost of Rs 4,441,000 by way of transportation and Rs 1,250,000 as annual fixed operating costs.
The management is contemplating to change the present schedule so as to attempt to reduce the total cost to the minimum, even considering the closure of some plant/s. You are required to formulate the problem as an IPP.

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Transportation Costs (in '000 Rs) per '000 Cars Warehouse Annual Production Annual Fixed Plant Capacity Operating 1 2 3 4 5 6 ('000 Cars) Costs ('000 Rs) 1 88 15 29 29 67 38 120 42 418 2 59 82 37 7 19 54 30 302 3 4 28 21 38 gg 80 21 30 18 57 15 27 NG 32 30 48 362 21 94 40 168 Annual Demand ('000 Cars) 21 21 12 12 17 6. 9 8 20 20