Device: Top-Freezer Refrigerator. Link: https://www.pacificsales.com/pdp/Samsung-21-1-Cu-Ft-Top-Freezer-Refrigerator-Stainless-Steel/5796734
Buying Price: $989.99 (as of 29 October 2017).
EnergyGuide Cost Link:
https://www.pacificsales.com/pdp/Samsung-21-1-Cu-Ft-Top-Freezer-Refrigerator-Stainless-Steel/5796734
Analysis
The formula for determining the total cost of the acquiring and maintaining the device is:
C (t) = C0+mtWhere C0 is the initial cost of the device, m is the annual energy cost and t is the time since the device was purchased.
C (t) = 989.99+57t; that is the cost function for operating the freezer refrigerator.
Average Cost per annum = AC (t) = (989.99 + 57t)/t = 989.99t+57Natural Domain of the average cost is all real numbers except zero; (-, 0)(0, )The restricted domain of the function = (0, )
The above graph shows a graph of the average cost function. The two lines are the asymptotes, indicating the values where the function approaches but never touches.
If another company offers to sell the same machine at 25 percent more, then the new price will be $1,237.49, and if the annual energy cost reduces by half, then it shall decline to $28.5.
The average cost per year for the adjusted prices will be;
AC (t) = 28.5 + 1237.49/t
The above is a graph of both old and new average cost per year, and it indicates the intersection and the horizontal intersections.
Questions to Answer
The domain has to be restricted because we are dealing with a faction with a variable as a denominator. Zero cannot be a denominator. Therefore the domain must be limited to exclude zero. We are dealing with the average cost of an item, which cannot be a negative value, which means for answers to be reasonable, all values in the domain must be restricted to be positive values.
The horizontal asymptote is a line where the function that is not continuous converges to, but do not touch. The function will keep moving closer and closer without touching it to infinity.
The points of intersection show that there are values of T (time), where both the old and new average cost per year is equal.
Device with Better Value
Device 1: C (t) = 989.99+57tDevice 2: C (t) = 1237.49 + 28.5t
For Device 1,
The cost is $1,046.99, $1,274.99 and 2,129.99 for 1, 5, and 20 years respectively.
For Device 2,
The cost is $1,265.99, $1,379.99, and $1,807.49 for 1, 5, and 20 years respectively.
From the above results, Device 1 is cheaper if kept for one or five years, whereas device 2 is cheaper when kept for 20 years.
A freezer refrigerator is one of the devices that met all the specified conditions for the project.
An online graphing calculator with the link; https://www.symbolab.com/
The graphing calculator is very accurate and has room to graph more than one function in the same graph.
There was no much difficulty other than choosing the device. The aim was to get one that had all the required information on the same page.
Next, probably determine the point of intersection for the two graphs.
Comparing the cost of buying, and maintaining a long-life device is critical. We all want to save, and if you want a device for ten years, you do not need to have one that will cost an arm and a leg. Therefore, you would need to consider the long-term cost of the product (Five things to consider when buying a Fridge Freezer, 2017). Find one with the lowest total cost for the ten years. For instance, in the above case, you would pick device one if you need to use it for five years but would choose the second device if you want to use it for twenty years.
References
Five things to consider when buying a Fridge Freezer. (2017). Argos.co.uk. Retrieved 30 October 2017, from http://www.argos.co.uk/static/StaticDisplay/includeName/fridge_freezer_guide.
Samsung - 21.1 Cu. Ft. Top-Freezer Refrigerator - Stainless Steel at Pacific Sales. (2017). Pacific Sales. Retrieved 30 October 2017, from https://www.pacificsales.com/pdp/Samsung-21-1-Cu-Ft-Top-Freezer-Refrigerator-Stainless-Steel/5796734
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