College Algebra & Trigonometry, 2018a

256 CHAPTER 4. FUNCTIONS
3) A power station and a factory are located on opposite sides of a river that
is 60 meters wide. The factory is 200 meters from the point on the shore directly
opposite the power station. A power line must be laid between the power station
and the factory. It costs $25 per meter to run the cable in the river and $20 per
meter to run the cable on the land. How much of the cable should be laid in the
river and how much should be laid on land to minimize the cost? Where should
the cable come ashore? What is the minimum cost?
Power Station
60 meters
200 meters
Factory
4) A freshwater pipeline is being constructed to an island that is 6 miles from
the mainland. The water source is 20 miles down the coast from the point on the
shore that is closest to the island. The cost of laying the pipeline along the shore
is $8,000 per mile while the cost of laying the pipeline in the water is $12,000
per mile. How much of the pipeline should be laid in the water and how much
should be laid on land to minimize the cost? Where should the pipeline leave the
shore? What is the minimum cost?
Water Source
20 miles
6 miles
Island