CleanAuto Inc. has four workers: Julie, Ian, Devon, and Thomas. CleanAuto Inc. provides two services: interior vacuuming and exterior wash. Julie can perform each of these tasks in one hour. Ian can do two interior vacuums or one exterior wash in one hour. Thomas can do two exterior washes or one interior vacuum in one hour. Devon only does exterior washes, and he can do an exterior wash in half an hour. Calculate the number of interior vacuums and exterior washes done in each of the following staffing scenarios in an eight-hour workday. Julie, Ian, and Thomas do only interior vacuuming, and Devon does only exterior washes. All four do only exterior washes. Julie, Ian, and Thomas each spend half their workday on each task, and Devon spends his entire day doing exterior washes. Create a graph of the production possibilities frontier (PPF) for this company using the answers from the calculations you completed for the above scenarios. Label each of the scenarios listed above as they appear on the PPF. The assignment should contain one graph ONLY. All four data points are plotted on the one graph. One half of all points (35.91) are for correct calculations of the four scenarios. Partial credit available for correct methodology but incorrect calculations. One half of total points are for a correct graph. Partial credit for correct methodology but incorrect plot points and Production Possibilities Curve. Make sure you draw a PPF after all four data points have been plotted.

Paper For Above instruction

This paper provides a comprehensive analysis of the production possibilities frontier (PPF) for Cleanauto Inc., considering various staffing scenarios involving the company's four workers: Julie, Ian, Devon, and Thomas. The analysis begins with calculating the outputs for each scenario based on worker capabilities, followed by graphically representing these possibilities on the PPF to illustrate the trade-offs in resource allocation between interior vacuuming and exterior washing services.

First, understanding the productivity of each worker is essential. Julie can perform either service in one hour, meaning she can complete one interior vacuum or one exterior wash per hour. Ian’s productivity is higher for interior vacuuming; he can do two vacuums or one exterior wash in an hour. Thomas can do two exterior washes or one interior vacuum per hour. Devon specializes solely in exterior washes, capable of completing one exterior wash in half an hour, translating to two exterior washes per hour.

In the fixed-duration, eight-hour workday, production outputs are calculated for each scenario:

Scenario 1: Julie, Ian, and Thomas do only interior vacuuming; Devon does only exterior washes

Julie: 1 vacuum/hour × 8 hours = 8 vacuums

Ian: 2 vacuums/hour × 8 hours = 16 vacuums

Thomas: 1 vacuum/hour × 8 hours = 8 vacuums

Total interior vacuums = 8 + 16 + 8 = 32

Devon: 2 exterior washes/hour × 8 hours = 16 washes

Total exterior washes = 16

Scenario 2: All four do only exterior washes

Julie: 0 exterior wash (since working only on vacuums)

Ian: 1 exterior wash/hour × 8 hours = 8 washes

Thomas: 2 exterior washes/hour × 8 hours = 16 washes

Devon: 2 exterior washes/hour × 8 hours = 16 washes

Total exterior washes = 8 + 16 + 16 = 40

Interior vacuums: none, since all focus on exterior washes

Scenario 3: Julie, Ian, and Thomas split their time equally between tasks; Devon works only on exterior washes

Julie: half the time on vacuums, half on washes: 4 vacuums and 4 washes in 8 hours

Ian: half the time on vacuums (2 vacuums/hour × 4 hours = 8 vacuums), half on washes (1 wash/hour × 4 hours = 4 washes)

Thomas: half the time on vacuums (1 vacuum/hour × 4 hours = 4 vacuums), half on washes (2 washes/hour × 4 hours = 8 washes)

Devon: entire day on washes (2 washes/hour × 8 hours = 16 washes)

Total interior vacuums: 4 + 8 + 4 = 16

Total exterior washes: 4 + 4 + 8 + 16 = 32

Scenario 4: All four do only exterior washes (full capacity)

Julie: 0 vacuums, 0 washes

Ian: 8 washes

Thomas: 16 washes

Devon: 16 washes

Total exterior washes = 8 + 16 + 16 = 40

Interior vacuums: none

Plotting these four data points on a graph with interior vacuums on the x-axis and exterior washes on the y-axis produces a clear PPF. The four scenarios provide the coordinates:

• Scenario 1: (32 vacuums, 16 washes)
• Scenario 2: (0 vacuums, 40 washes)
• Scenario 3: (16 vacuums, 32 washes)
• Scenario 4: (0 vacuums, 40 washes)

Connecting these points with a smooth curve depicts the company's production trade-offs, illustrating the maximum possible output combinations given resource constraints. The PPF curve demonstrates the opportunity costs involved in reallocating labor between vacuuming and washing services, highlighting the most efficient production points and potential for further specialization.

Graph of PPF

Scenario 2

Scenario 3

Scenario 1

Scenario 4

The plotted points effectively demonstrate the trade-offs in resource allocation for Cleanauto Inc., emphasizing how workforce specialization and time division influence maximum output possibilities in both services.

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