"The Grains" is a leading grower of wheat with three large wheat crops scattered around the Punjab province of Pakistan in the cities of Lahore, Okara and Sahiwal. "The Grains" currently has 90,000 wheat bags at the fields in Lahore, 120,000 wheat bags at the fields in Okara, and 180,000 wheat bags at Sahiwal. "The Grains" has wheat processing plants in Pasroor, Kasur and Chakwal with processing capacities to handle 85,000, 120,000 and 200,000 wheat bags respectively. "The Grains" contracts with local loading/unloading company to transport its wheat from fields to the processing plants. The company charges a flat rate for every kilo-meter that each wheat bag transported. Each kilometer a wheat bag travels is known as wheatbag-km. The following table summarizes the distances (in km) between the crop fields and processing plants.

Distance (in km) between the crops and processing plants

Crop Fields Pasroor Kasur Chakwal

Lahore 40 50 120

Okara 40 30 150

Sahiwal 100 90 210

"The Grains" wants to determine how many wheat bags to ship from each crop field to each processing plant to minimize the total cost.