As count engineer, it is your responsibility to design a master plan for refuse disposal for a 4-city area. All waste is delivered to one of two transfer stations where it is compacted and placed into large transport vehicles for shipment to one of three landfills. Each transfer station can process 700 tons of refuse daily, and the capacities of the three landfills are 500, 420, and 600 tons of waste per day, respectively. All shipping costs are directly proportional to the travel distances shown in the table below, but shipments from the transfer stations are 50% lower per mile than are those of the rout trucks that transport refuse directly from residence to transfer station:

For example, a unit of refuse transported by route truck from Pleasantville 10 Transfer Station Number I travels a distance of 45 miles. If that unit of refuse is then transported to Landfill No.3, it wills he moved another 146 miles but at a 50% lower unit transport cost. Pleasantville generates 205 tons of waste each day, and Landfill No. 3 can process a total of 600 tons per day from both transfer stations.
Formulate a linear program that will help you plan a policy for managing the disposal operation at least cost.

Transport Distances From City Daily Refuse Production Transfer Station 1 Transfer Station 2 Pleasantville 205 45 58 369 Odorsburg 39 79 Scentington 340 74 93 Smelberry 408 25 44 To Landfill Daily Capacity Landfill No. 1 500 157 175 Landfill No. 2 420 234 136 Landfill No. 3 600 146 192