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I see you've uploaded an image showing a problem about selecting between three machine types (A, B, and C) for a manager's decision, based on purchasing and operating costs. The task requires calculating both total purchasing and operating costs for each machine.

Here's the breakdown:

### Part a: Total Processing Time and Number of Machines Needed
1. You are asked to calculate the total processing time in minutes for each machine type to meet product demands.
2. Then, using the available hours per year (8 hours/day, 240 days/year), determine how many machines are required.
3. Based on the results, compute the total purchasing costs for each type of machine.

This part seems to be completed, with the rounded number of machines required:
- Machine A: 3 machines ($210,000 total)
- Machine B: 4 machines ($240,000 total)
- Machine C: 3 machines ($150,000 total)

### Part b: Calculate Total Costs Including Hourly Operating Costs
1. **Hourly Operating Costs**:
   - A: $13/hour
   - B: $11/hour
   - C: $10/hour
2. The machine operates for 8 hours/day, 240 days/year, so each machine runs for:
   \[
   8 \, \text{hours/day} \times 240 \, \text{days/year} = 1,920 \, \text{hours/year}
   \]
3. The total annual operating cost for each machine type would be the number of machines multiplied by the hourly cost and annual hours of operation.

Let me now calculate these values for each machine type in Part b.The total costs for each machine type, including both the purchasing and operating costs, are:

- **Machine A**: $284,880
- **Machine B**: $324,480
- **Machine C**: $207,600

Based on these calculations, Machine C has the lowest total cost, which aligns with the decision made in the earlier steps.

Would you like more details on how these were calculated, or do you have any further questions?

Here are 5 related questions to explore:
1. What would be the impact on total costs if the number of operating hours per day increased?
2. How would the result change if the hourly operating cost for Machine C increased to $12 per hour?
3. Could leasing the machines be more cost-effective compared to purchasing?
4. What would happen to the total cost if annual demand increased by 10% for all products?
5. How would the decision change if one machine type had a downtime rate of 10%?

**Tip**: Always verify both fixed (purchasing) and variable (operating) costs when making investment decisions involving machinery.

A manager must decide which type of machine to buy, A, B, or C. Machine costs per unit and processing times for different products are given. The goal is to compute total processing time, the number of machines required, and total costs including both purchasing and hourly operating costs.

In this cost optimization problem, learn how to determine the best machine type for a manager by calculating total processing time, the number of machines required, and total purchasing and operating costs. Explore formulas to make cost-effective decisions for machine investments.

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