Minimum-Cost Analysis
A continuous electric current of 2,000 amps is to be transmitted from a generator to a transformer located 200 feet away. A copper conductor can be installed for $6 per pound, will have an estimated life of 25 years, and can be salvaged for $1 per pound. Power loss from the conductor will be inversely proportional to the crosssectional area of the conductor and may be expressed as 6.516/A kilowatt, whereAÂ is in square inches. The cost of energy is $0.0825 per kilowatt-hour, the interest rate is 11%, and the density of copper is 555 pounds per cubic foot.
(a) Calculate the optimum cross-sectional area of the conductor.
(b) Calculate the annual equivalent total cost for the value you obtained in part (a).
(c) Graph the two individual cost factors (capital cost and power-loss cost) and the total cost as a function of the cross-sectional area A, and discuss the impact of increasing energy cost on the optimum obtained in part (a).
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