Cost Efficiency Of Two Computers!

By: Smita, Period 1 #25

Situation

A school is deciding to buy a long term cost efficient computer for it's office. The school is planning to use the computer for 8 hours each day. (The cost of electricity is $0.1/kwh).

They have two options between two models :


  • Computer A costs $700 (but uses 0.143 kilowatts/hour); which will cost about $42.00 each year. (0.143*8*365*0.1=$42)


  • Computer B costs $550 (but uses 0.246 kilowatts /hour); which will cost about $72.00 each year. (0.236*8*365*0.1=$72)



The school wants to buy a long term computer which will last at least 10 years.

Which computer should the School purchase based on the cost efficiency of the computers?

The Classification Of The Variables

The two variables are the number of years and the cost.

Number Of Years is the independent variable and will be represented using the variable y

The Cost is the dependent variable and will be represented by using the variable C

Table Of Values

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Equations:

In y=mx+b Form

m: (slope) the yearly cost

b: (y-intercept) initial cost of the computer

y:(dependent variable)total cost; represented by the variable C

x:(independent variable)number of years; represented by the variable y


Computer A: C=42y+700

Computer B: C=72y+550


(Both equations represent partial variation)

Graph

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P.O.I. & The Significance Of the Data

Point of Intersection is (5, 910)

The point of intersection satisfies both equations:

Computer A:

C=42y+700

(Substitute value of C and y)

910=42(5)+700

=910=210+700

=910=910


Computer B:

C=72y+550

(Substitute value of C and y)

910=72(5)+550

=910=360+550

=910=910


The significance of the Point Of Intersection in this situation is that both computers will cost the same at the same point in time. Thus in 5 years both computers will cost $910.

Significance Of The Data:

  • If the school uses the computer for 5 years it would cost both Computer A and Computer B $910.
  • If the school is planning to use the computer for less than 5 years it would be inexpensive to purchase Computer B.
  • Although, if the school is planning to use the computer for more than 5 years it would be inexpensive to choose Computer A.

Conclusion:

Therefore, the school should purchase Computer A because they want a computer to use for at least 10 years and in 10 years Computer A is more cost efficient than Computer B!