given the high cost gassoline, automobile owners are constantly searching for wa
ID: 3148759 • Letter: G
Question
given the high cost gassoline, automobile owners are constantly searching for ways of economizing on driving expenses. One costly alternative for many persons is to purchase a new carwhich gets significantly better gesoline millage then does thier present car. chamberlain developeda mathimatical formula to calculate how many years a person would have to drive a new car to make the gasoline savings offset the cost of trading in the old car and buying a new car. the varriables to be used in this analysis are:
= number of years to justify the purchase of new car
m= gasoline millage of present car, miles per gallon
n=gasoline millage of new car, milag per gallon
c= net cost of new car
d= avg number of miles driven per year
p= gasoline price per gallon
chamberline determines this "breakeven" period using the genral relationship
cost of gasoline of present car during break even period = cost of gasoline of new car during break even period + net cost of new car
or F-old (Y)=F-new(Y)
1. using the varriables defined previousely, determine the expression for F-old(Y) & F-new(Y)
2. set F-old(Y) equals to F-new(Y) and drive the genral formula for breakeven period Y.
3. determine the breakeven period if the present car has a value of $8,000 and gets 14 miles per gallon. the new car has a purchase cost of $16,000 and gets an estimated 46 miles per gallon. Gasolline prices are currently $1.50 per gallon. Assume annual millage of 24,000 miles.
5. Rework part 1-3 if the unknown is the x, the total miles driven. that is suppose we wish to develope a formula that allows one to determine the number of miles. rather then number of years. a new car would have to driven. average millage per day d is not part of this modlel.
6. lis tassumption of this model. what assumptions are unrealistic? whyy?what cost factors have not been considered?
Explanation / Answer
Y = Breakeven Period
m = milege present car ; n = milege new car
c = net cost of new car
p = gasolin price per gallon, d = avg miles covered per year
After Y years
Total distance covered = d*y
WIth Old Car
Total Cost = cost of gasoline = (Distance Covered / Mileage)*Price per gallon = (dy/m)*p
With New car
Total cost = cost of gasoline + cost of car = c + dyp/n
2) c + dpy/n = dpy/m
c = dpy(1/m - 1/n)
c*(mn/n-m) = dpy
y = (c/dp)*(mn/n-m)
3) c = cost of new car = Cost of new - value of old = $8,000
y = {8000/24000*1.5}{46*14/(46-14)}
= 46*14/(4.5*32)
= 4.47 years
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