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The problem presented relates to determining the optimal number of spare parts for a turbine, considering costs of carrying, disposal, and shortage, while referencing a Poisson distribution for part demand.

**Part a.** asks for the optimal number of spare parts to order, and based on the response, the answer is already provided as **10 spare parts**.

**Part b.** involves determining the range of shortage costs where carrying no spare parts is the best strategy, and it requires rounding the answer to two decimal places. This calculation likely depends on minimizing total cost, where shortage cost \( C_s \) (the cost incurred when not having a spare part) plays a crucial role.

### Step-by-step approach for part b:

1. **Use Table C**: The table given contains values for the cumulative Poisson distribution for different \( \lambda \) values (which would likely be the mean of 3.4 parts) and different inventory levels.
   
2. **Condition for "no spare parts"**: We need to find at what shortage cost level \( C_s \), carrying no spare parts (inventory of 0) becomes more favorable than ordering any spare parts. This can be done by comparing the carrying costs with the potential shortage costs.

3. **Refer to \( \lambda = 3.4 \)**: Since the mean number of parts needed follows a Poisson distribution with a mean of 3.4, focus on the row in Table C that corresponds to \( \lambda = 3.4 \). We must use this to calculate the expected costs.

Since the table and specific formulas aren't fully visible here, I would calculate the shortage cost based on minimizing the total expected cost, which includes shortage and holding costs, along with using the cumulative Poisson probabilities.

If you would like a detailed walkthrough of how to compute the shortage cost or clarify any particular table entry, please let me know.

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Would you like more details on solving this problem or help with anything else?

### Related Questions:
1. How is the Poisson distribution used to model part demand in this context?
2. What is the formula for calculating total expected costs (including holding and shortage costs)?
3. What are the steps to compute the cumulative Poisson probabilities from Table C?
4. How does the shortage cost affect the decision to carry spare parts?
5. How would the solution change if the mean demand were different (e.g., 5 parts instead of 3.4)?

#### Tip:
When solving problems like this, always balance holding costs and shortage costs to find the optimal inventory level.

A public utility intends to buy a turbine as part of an expansion plan and must decide on the number of spare parts to order. What is the optimal number of spares and the range of shortage cost where carrying no spare parts is the best strategy?

Learn how to determine the optimal number of spare parts for a turbine using the Poisson distribution model. This problem also explores calculating shortage costs to minimize inventory holding and shortage expenses, suitable for engineering and operations research students.

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