Suppose that chemical X is manufactured using a raw material B that is available from a location called the “mine.” Production of one ton of X requires 1/3 of a ton of B. A firm called X Enterprises, which has a contract to deliver 30 tons of X to a location called the “market,” is trying to decide where to locate its plant. The mine and the market are 50 miles apart. Overland shipment of both X and B costs $2 per ton per mile shipped. However, additional costs must be incurred because a river passes between the mine and the market, and the river has no bridge. Goods must be loaded onto barges to cross the river, which is located 16 miles from the mine. Barge operators charge $1 per ton of X shipped across the river. However, since the input B is highly toxic when mixed with water, barge operators must charge an extremely high price to transport B across the river. This price defrays the cost of insurance that the operators must carry to meet liability claims should they accidentally pollute the river with their cargo. The cost of shipping one ton of B across the river is $195.
Four locations for firms are:
mine, market, mine side of the river, and market side of river
(1) Using the above information, find the transport-cost-minimizing location for X Enterprises, which is the location ------------- .
(Assume that the width of the river is negligible so that it can be ignored.)
(2) The input cost of the location you filled in above for the firm is --------------, and the output cost is ------------, and the total cost is ------------.
(3) Explain your results in question 3.1 intuitively.
This is the only information I got.
Any other problem is ignorable.