A factory which uses a large amount of coal is situated between two collieries, X and Y, with both being at a distance of 5 and 10 kms, respectively, from the factory. A fleet or lorries of 5 tonnes...

A factory which uses a large amount of coal is situated between two collieries, X and Y, with both being at a distance of 5 and 10 kms, respectively, from the factory. A fleet or lorries of 5 tonnes carrying capacity is used for collecting coal from the pitheads. The lorries average a speed of 20 kilometres per hour when running and generally take 10 minutes to unload in the factory premises. At colliery X, loading time averages 30 minutes per load, while at colliery Y it is 20 minutes per load.

Driver’s wages, licences, insurance, depreciation, garage, and similar charges cost `60 per hour operated. Fuel, oil, tyres repairs and similar charges cost `6 per km run.

Draw up a statement showing the cost per-tonne-kilometre of carrying coal from each colliery. If the coal is of same quality and price at pithead, which of the collieries should the company prefer to make purchases?