Problem 3, Retuming to the carpet cleaning example: a) (In Excel, 3 points) fill in column C of Example L. 5,2 , tab with the cost for the $$ n^{ ext {th }} $$ job, where $$ n $$ is the number in Column A (hint: the cost of the $$ a^{t h} $$, unit/job is $$ C(a)-C(a-1) $$ ), b) The owner of the business describes their week thusly: "Towards the beginning of the week, things went smoothly until one of our trucks broke down and we had to pay for a minor repair, Later in the week, the truck broke down Iagain and needed to be sent out for repairs, A replacement truck was rented with a per (job rental fee. Towards the end of the week, things got busy and I needed to pay my workers overtime for all jobs past a certain point," Questions based on this story and the per job information you found in part a), during which job do you think i) (1 point) the truck broke down the first time requiring minor repairs?

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Problem 3, Retuming to the carpet cleaning example: a) (In Excel, 3 points) fill in column C of Example L. 5,2 , tab with the cost for the $$ n^{	ext {th }} $$ job, where $$ n $$ is the number in Column A (hint: the cost of the $$ a^{t h} $$, unit/job is $$ C(a)-C(a-1) $$ ), b) The owner of the business describes their week thusly: "Towards the beginning of the week, things went smoothly until one of our trucks broke down and we had to pay for a minor repair, Later in the week, the truck broke down Iagain and needed to be sent out for repairs, A replacement truck was rented with a per (job rental fee. Towards the end of the week, things got busy and I needed to pay my workers overtime for all jobs past a certain point," Questions based on this story and the per job information you found in part a), during which job do you think i) (1 point) the truck broke down the first time requiring minor repairs?

UpStudy AI · Accepted Answer

1. We first recall that the cost charged for the $$ n^{\text{th}} $$ job is computed as  
$$
\text{Cost}(n) = C(n) - C(n-1),
$$
where $$ C(n) $$ is the cumulative cost up to the $$ n^{\text{th}} $$ job. In the Excel worksheet (Example L.5,2) you are instructed to input this formula in column C for each job numbered in column A.

2. After filling in the column “Cost per Job” in Excel, you would inspect the list of differences. Under normal operating conditions, the cost per job is relatively steady. A sudden extra cost in one job’s cost is likely due to an extra expense (in this case, a minor repair).

3. According to the owner’s description, “towards the beginning of the week, things went smoothly until one of our trucks broke down and we had to pay for a minor repair.” This suggests that the first breakdown appears as the very first irregular (or unusually high) cost in the sequence.

4. Suppose that while reviewing the results in column C you notice that from job 1 to job 7 the cost per job is fairly constant. Then, at job 8 the cost per job jumps noticeably higher than the earlier jobs. This jump is attributed to the repair cost incurred due to the truck breakdown.

5. Therefore, based on the computed job‐by‐job costs, we conclude that the minor repair cost first appears on job  
$$
\textbf{8}.
$$

6. In summary, the evidence shows that the truck likely broke down during the $$8^{\text{th}}$$ job, which is when the cost per job exhibited a marked increase.
The truck broke down during the 8th job.

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