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 36,000-Btu central air conditioner of each type are given in Table 1. These costs do not include maintenance charges or changes in electricity prices.
Table 1 36,000 Btu Central air Conditioner
| Energy-Efficient Model | Conventional Model |
Initial cost | $4,000 | $2,700 |
Total capacity | 36,000 Btu | 36,000 Btu |
Annual cost of electricity | $932 | $1,332 |
(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.
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