Identify the network approach and solve the following problem I have just purcha
ID: 356364 • Letter: I
Question
Identify the network approach and solve the following problem I have just purchased a new car for $12,000. The cost of maintaining a car during a year depends on the age of the car at the beginning of the year, as given in Table 1. To avoid the high maintenance costs associated with an older car, I may trade in my car and purchase a new car. The price I receive on a trade in depends on the age of the car at the time of the trade-n (see Table 2). To simplify the computations, we assume that at any given time, it costs $12,000 to purchase a new car. My goal is to minimize the net cost incurred during the next five years. Table 1 Car Maintenance problems 4 Age of car Annual Maintenance $2000 $4000 $5000 $9000 $12000 cost (cumulative) Table 2 Car Trade-in Price 4 Age of car Trade-In Price $7000 $6000 $2000 $1000 $0Explanation / Answer
Let us compute the various scenarios available here:
The first step is to compute the per year maintenance costs, as all costs given are cumulative:
The calculation is simple - the maintenance cost for year 2 is $4000 - $2000 = $2000. Cumulative cost of $4000 for year 2 means that the total cost of maintenance for years 1 & 2 together is $4000. Now, we already know that the cost of maintenance for the first year is $2000, right? Hence, the cost for the second year alone is the difference between the two.
Basically, the nth year maintenance cost = Cumulative cost for year n - cumulative cost for year (n-1)
Now, let us compute the various scenarios:
We buy the car and do not trade in for 5 years:
In this case:
Cost of car: $12,000
Cost of maintaining the car for 5 years: $12000
Hence, total costs incurred = $12000 + $12000 = $24,000
Let us assume, now, that we trade in the car in year 1:
In this case:
Cost of buying the car in year 0: $12000
Cost of maintaining the car for year 0: $2000
Now, we buy a new car in year 1, right? The trade in price of the car in year 1 is given as $7000. This means, we will get $7000 for our old car. Since a new car costs $12000, the effective price to pay = $12000 - $7000 = $5000
Hence, cost of buying the traded in car = $5000
Now, we will have to maintain the new car for only 4 years, right? As we have already maintained our old car for 5 years.
Cost of maintenance of the car for the four years = $9000 (given in the table)
Total costs = $9000 + $5000 + $12000 + $2000 = $28000
Hence, the total five year costs if we trade the car in the 1st year = $28000
Similarly, you can compute/prepare the total costs for all the 5 scenarios (trading in the car in the 2nd year, 3rd year, 4th year and 5th year).
The results should look like this
Clearly, you can see that the best option comes if we trade the car in during year 2 - this gives us a cost of $27000.
However, we have already computed in #1 that the cost of just maintaining a new car is $24000.
Hence, the best option is to just buy a new car and maintain it for 5 years - this can be done at a cost of $24000. The second best option is to trade in the car in year 2 - this can be done at a total cost of $27000.
Age AMC Cost/year 0 2000 2000 1 4000 2000 2 5000 1000 3 9000 4000 4 12000 3000