Most appliance manufacturers produce conventional and energy-efficient models. The energy-efficient models are more expensive to make but cheaper to operate. The costs of purchasing and operating a 36,000-Btu central air conditioner of each type are given in Table 9. These costs do not include maintenance charges or changes in electricity prices.

(A) Express the total cost Ce(x) and the average cost e(x) = Ce(x)/x of purchasing and operating an energy-efficient model for x years.
(B) Express the total cost Cc(x) and the average cost c(x) = Cc(x)/x of purchasing and operating a conventional model for x years.
(C) Are the total costs for an energy-efficient model and for a conventional model ever the same? If so, when?
(D) Are the average costs for an energy-efficient model and for a conventional model ever the same? If so, when?
(E) Find the limit of each average cost function as x-> ˆž and discuss the implications of the results.

Transcribed Image Text:

Table 9 36,000 Btu Central Air Conditioner Energy-EficientConventional Model Model Initial cost Total capacity Annual cost of electricity 4,000 36,000 Btu $932 $2.700 36,000 Btu $1.332