To calculate the implied utilization of the resource, we first need to understand the total demand on the resource and the resource's capacity.

Given:

• Type 1 (first client type):
  • Processing time = 2.8 hours
  • Demand = 0.7 clients per hour
• Type 2 (second client type):
  • Processing time = 16 hours
  • Demand = 0.42 clients per hour
• Number of workers = 9

Step 1: Calculate the total demand for the resource.

The total demand on the resource is the sum of the demand from both types of clients, weighted by the amount of time it takes to process each client.

For Type 1:

Demand for Type 1 clients = $0.7 \text{ clients/hour} \times 2.8 \text{ hours/client} = 1.96 \text{ hours/hour}$.

For Type 2:

Demand for Type 2 clients = $0.42 \text{ clients/hour} \times 16 \text{ hours/client} = 6.72 \text{ hours/hour}$.

Thus, the total demand on the resource is: $1.96 \text{ hours/hour} + 6.72 \text{ hours/hour} = 8.68 \text{ hours/hour}.$

Step 2: Calculate the resource's capacity.

The resource's capacity is the total number of workers multiplied by the time each worker can work per hour. Since there are 9 workers and each worker can work 1 hour per hour, the capacity is:

$9 \text{ workers} \times 1 \text{ hour/hour} = 9 \text{ hours/hour}.$

Step 3: Calculate the implied utilization.

The implied utilization is the ratio of the total demand to the capacity of the resource: $\text{Implied utilization} = \frac{\text{Total demand}}{\text{Capacity}} = \frac{8.68 \text{ hours/hour}}{9 \text{ hours/hour}} = 0.9644.$

Converting this into a percentage: $0.9644 \times 100 = 96.4\%.$

Thus, the implied utilization of the resource is 96.4%.

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Would you like further clarification or details? Here are some related questions you might find useful:

1. How would the implied utilization change if we had more workers?
2. What impact would increasing the demand for Type 2 clients have on the implied utilization?
3. If the processing time for Type 1 clients were reduced, how would the utilization be affected?
4. What is the difference between implied utilization and actual utilization?
5. How can we optimize the number of workers to match the demand for both client types?

Tip: When dealing with multiple types of demand, it's essential to break down the demand contributions from each type to accurately calculate total resource utilization.