A department works one eight-hour shift, 250 days a year. How many machines are needed to handle the required volume, given the following processing times?

| Product | Annual Demand | Process Time per Unit (hr) | Total Processing Time Needed (hr) |
|---------|---------------|----------------------------|-----------------------------------|
| 1 | 400 | 5.0 | 2000 |
| 2 | 300 | 8.0 | 2400 |
| 3 | 700 | 2.0 | 1400 |

In order to handle the volume, the department would need at least 4 machines. This is estimated by dividing the total processing time required (5800 hours/year) by the hours available per machine per year (2000 hours/year).

To calculate the number of machines needed, we have to determine the total processing time required annually and then compare it to the available work time. Given that the department works one eight-hour shift per day for 250 days a year, the total hours available per year would be 8 hours/day * 250 days/year = 2000 hours/year.

Now, we need to add up the annual processing time needed for all products. This is:

Product 1: 400 units/year * 5.0 hours/unit = 2000 hours/year
Product 2: 300 units/year * 8.0 hours/unit = 2400 hours/year
Product 3: 700 units/year * 2.0 hours/unit = 1400 hours/year

This gives a total demand of 2000+2400+1400 = 5800 hours/year.

Therefore, the minimum number of machines needed would be the Total processing time required ÷ Hours available per machine per year. If one machine only can make one type of product, we need 1 machine for Product 1, 2 machines for Product 2 (since 2400/2000 = 1.2 rounds to 2), and 1 machine for Product 3. So, we would need a total of 4 machines.

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