Question

Let's assume that we have just purchased a new car (or machine) for $12,000 at time 0 . The cost of maintaining the car during a year depends on the age of the car at the beginning of the year, as given in the table below. - In order to avoid the high maintenance cost associated with an older car, we may trade in the car and purchase a new car. The trade-in prices are also given in the table. To simplify the computations we assume that at any time it costs $12,000 to purchase a new car. Our goal is to minimize the net cost incurred during the next five years. Let's formulate this problem as a shortest path problem. Our network will have six nodes. Node i is the beginning of year i and for i

Answer 1

The probability that a car required over $300 for maintenance during its first year is 13.5%

Step-by-step explanation:

The cost of maintaining a car during its first year is approximately exponentially distributed with a mean of $150. To find the probability that a car required over $300 for maintenance during its first year, we can use the exponential distribution formula:

P(X > 300) = e-300/150 = 0.135

This means that there is a 13.5% probability that a car will require over $300 for maintenance during its first year.