During the campus Spring Fling, the bumper car amusement attraction has a problem of cars becoming disabled and in need of repair. Repair personnel can be hired at the rate of $20 per hour, but they only work as one team. Thus, if one person is hired, he or she works alone; two or three people work together on the same repair.

One repairer can fix cars in an average time of 30 minutes. Two repairers take 20 minutes, and three take 15 minutes. While these cars are down, lost income is $40 per hour. Cars tend to break down at the rate of two per hour.

Management is trying to decide how many repair persons to hire, and has asked you for cost data.

What is the total hourly cost with one repair person?

multiple choice
$∞
$60
$140

What is the total hourly cost with two repair persons?

Note: Round your answer to the nearest dollar amount.



What is the total hourly cost with three repair persons?

Note: Round your answer to the nearest dollar amount.



How many repairers should be hired?





To determine how many repair personnel to hire, we need to compute the **total hourly cost** for each scenario, which consists of two components:
1. **Labor cost**: the cost of hiring the repairers.
2. **Lost income cost**: the cost due to cars being down for repairs.

### Key Information:
- **Labor cost per hour**: $20 per repair person.
- **Lost income**: $40 per hour per car down.
- **Cars break down at 2 per hour**.
- Repair time per car depends on the number of repairers:
  - 1 repair person: 30 minutes per car.
  - 2 repair persons: 20 minutes per car.
  - 3 repair persons: 15 minutes per car.

### Step 1: Calculate the total hourly cost with **1 repair person**.

- **Repair rate** with 1 repair person: 1 car takes 30 minutes, so 2 cars take 1 hour.
  - This exactly matches the breakdown rate of 2 cars per hour.
  - Since repairs keep up with the breakdown rate, no backlog forms.
- **Labor cost**: $20/hour for one person.
- **Lost income cost**: Since repairs keep up with the breakdown rate, cars are repaired without delay, so no cars are down at any point.
  - Therefore, there is no lost income.
- **Total hourly cost** = **Labor cost** + **Lost income cost** = $20 + $0 = **$20**.

However, it seems like the answer choices given were $∞, $60, or $140. Let’s reanalyze this choice based on the assumption that the work process might involve backlog or inability to keep up in real scenarios.

The answer for **one repair person** might need to consider costs beyond just efficiency rates, but based on given data, we should infer the correct breakdown for all cases. Let’s first move onto **two repair persons** below

During the campus Spring Fling, the bumper car amusement attraction has a problem of cars becoming disabled and in need of repair. Repair personnel can be hired at the rate of $20 per hour, but they only work as one team. Thus, if one person is hired, he or she works alone; two or three people work together on the same repair.

One repairer can fix cars in an average time of 30 minutes. Two repairers take 20 minutes, and three take 15 minutes. While these cars are down, lost income is $40 per hour. Cars tend to break down at the rate of two per hour.

Management is trying to decide how many repair persons to hire, and has asked you for cost data.

What is the total hourly cost with one repair person?

multiple choice
$∞
$60
$140

What is the total hourly cost with two repair persons?

Note: Round your answer to the nearest dollar amount.

What is the total hourly cost with three repair persons?

Note: Round your answer to the nearest dollar amount.

How many repairers should be hired?

Analyze the optimal number of repairers needed for bumper car maintenance at a campus event. Understand cost breakdown including labor and lost income, with formulas for calculating the hourly total cost for different repair team sizes. Ideal for students studying business or economics.

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