Problem

Energy costs. Most appliance manufacturers produce conventional and energy-efficient model...

Energy costs. 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 23-cubic-foot refrigerator of each type are given in Table 1. These costs do not include maintenance charges or changes in electricity prices.

Table 1 23-ft3 refrigerators

	Energy-Efficient Model	Conventional Model
Initial cost	$950	$900
Total volume	23 ft3	23 ft3
Annual cost of electricity	$56	$66

(A) Express the total cost Ce(x) and the average cost of purchasing and operating an energy-efficient model for x years.
(B) Express the total cost Cc(x) and the average cost 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 → ∞ and discuss the implications of the results.