何先生想要更换他办公大楼内的所有 60 台空调。 他在两个品牌的空调之间进行抉择。 这两个品牌空调的信息如下表所示。 2022 年 7 月 1 日起的电费标准如下表所示。 何先生办公大楼内空调的使用情况如下表所示。

1. Calculate the total usage of all units in one week.

Monday usage:
$50 \times 8 = 400\text{ h}$

Tuesday to Friday usage:
$4 \times 60 \times 6 = 1440\text{ h}$

Total usage per week:
$400 + 1440 = 1840\text{ h}$

2. Multiply weekly usage by the number of operating weeks in a year.

Usage for $51$ weeks:
$1840 \times 51 = 93840\text{ h}$

1. Calculate the purchase cost for 60 units of each brand.

Samsing purchase cost
$=60\times 1388=\char36{}83\,280$

Potasonic purchase cost
$=60\times 740=\char36{}44\,400$

2. Calculate the 4-year electricity cost for Samsing.

From part (a), total yearly usage of all air conditioner units is $14\,790$ h.

Samsing power consumption per unit $=3$ kW.

Energy used in 4 years
$=14\,790\times 3\times 4=177\,480\text{ kWh}$

Tariff with GST $=32.28$ cents per kWh $=\char36{}0.3228$ per kWh.

Electricity cost
$=177\,480\times 0.3228=\char36{}57\,290.544$

3. Calculate the 4-year electricity cost for Potasonic.

Potasonic power consumption per unit $=3.5$ kW.

Energy used in 4 years
$=14\,790\times 3.5\times 4=207\,060\text{ kWh}$

Electricity cost
$=207\,060\times 0.3228=\char36{}66\,838.968$

4. Calculate the chargeable servicing cost over 4 years for each brand, taking warranty into account.

Warranties cover servicing and maintenance.

For Samsing, warranty is for 2 years, so servicing is chargeable for years 3 and 4 only.

Samsing servicing cost
$=2\text{ years}\times 2\text{ servicings per year}\times \char36{}2100=\char36{}8400$

For Potasonic, warranty is for 3 years, so servicing is chargeable for year 4 only.

Potasonic servicing cost
$=1\text{ year}\times 4\text{ servicings per year}\times \char36{}2100=\char36{}8400$

5. Compare the total 4-year costs and make a justified decision.

Samsing total cost
$=83\,280+57\,290.544+8400=\char36{}148\,970.544$

Potasonic total cost
$=44\,400+66\,838.968+8400=\char36{}119\,638.968$

Since $119\,638.968<148\,970.544$, Potasonic has the lower cost after 4 years.

1. State one reasonable assumption used in the cost comparison.

Assume that the electricity tariff remains constant at $32.28$ cents per kWh throughout the 4 years.