Coal and iron ore are produced in a mine located on the west. Amarket located...

Coal and iron ore are produced in a mine located on the west. A market located on the est demands steel. A plant must be located between the mine and the market to produce steel from coal and ore. Assume that 2 tons of coal and ore are needed to produce 1 ton of steel. The market is 1,000 miles away from the mine. Transportation takes cost at $m per ton-mile for coal&ore and $n per ton-mile for steel. Let X denote the distance from the mine to the plant.

A. Describe the total transportation cost (TTC) which depends on m, n, x

B. If m < 2n, where should the plant be located to minimize TTC?

Solutions

Expert Solution

Answer : Total Transportation Cost

Total distance of mine to market is 1000 miles and plant is at centre that is at X mile from mine. Distance from plant to market is (1000-x). Hence cost of transportation of 2 Tons of coal and ore from mine to plant is total 2 tons × x miles × m = $ 2xm

Transportation cost from plant to market of 1 Ton of steel is 1 × n × (1000 - x ) = 1000n-nx

Total Transportation cost is (2xm + (1000-x ) N

Answer : As m and n costs are not given if it is assumed to be same then m < 2n means transportation cost of steel is doubled as compare to transportation cost of ore and coal hence plant should be located at 1000 miles so that to save Total Transportation cost.

Rahul Sunny answered 2 years ago

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