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# Basic Maths Question

barry1010 | 17:40 Tue 25th Jun 2024 | How it Works

I've owned up before to being rubbish at simple maths so I need help.  This is not hypothetical so it is crucial the information is correct.

A planned business will operate 24/7 365 days a year.  It will need two members of staff in attendance at all times.  Assuming a 38 hour week, how many staff will the business need?  Breaks can be staggered and one person can cover those times.

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A bit too complicated for me to tackle. Do companies allow for sick leave, holiday leave, gaps when people are sacked or leave the company and new staff has to be found? I don't think there is a simple mathematical answer.

At least 8 people.

There are 168 work hours per week.

Assuming 38 hrs per staff member. 168/38 = 4.4 members of staff.

But as Athiest says that is at its' most basic and doesn't account for illness, holidays, other works absence.

Question Author

Annual leave and sick leave would have to be taken in to account - this would not be suitable for temps or part timers.

Question Author

Thanks for all the answers, it is trickier than I thought.  To cover holiday and sick leave it seems that 11 people would be the sensible minimum.

A wage bill of at least £4540 a week on minimum wage.

Sorry, I'm an idiot.....

My figure is for one person so you will need a minimum of 8.8 people to cover any single week.

I'll say 12.

Question Author

I think you are probably right, dave.  Maternity leave could throw a spanner in the works as could long term sickness.  It's a minefield

Chatgpt thinks its this..  check carefully but it does look logical

To determine the number of staff required for a business operating 24/7 with two members of staff on duty at all times, taking into account a 38-hour work week and breaks and holidays, we'll go through the following steps:

1. **Calculate Total Hours Required Per Year**:
- There are 24 hours in a day and 365 days in a year.
- $$24 \text{ hours/day} \times 365 \text{ days/year} = 8,760 \text{ hours/year}$$
- Since two staff members are needed at all times:
- $$8,760 \text{ hours/year} \times 2 = 17,520 \text{ staff-hours/year}$$

2. **Calculate Working Hours Per Staff Member Per Year**:
- Each staff member works 38 hours per week.
- $$38 \text{ hours/week} \times 52 \text{ weeks/year} = 1,976 \text{ hours/year}$$

3. **Adjust for Breaks and Holidays**:
- In the UK, full-time employees are entitled to 28 days of holiday per year.
- Holidays equate to $$28 \text{ days} \times 7.6 \text{ hours/day} = 212.8 \text{ hours/year}$$ (assuming an 8-hour workday for simplicity).
- The actual working hours per staff member per year:
- $$1,976 \text{ hours/year} - 212.8 \text{ hours/year} = 1,763.2 \text{ hours/year}$$

4. **Calculate Total Number of Staff Required**:
- To cover the total required staff-hours per year:
- $$\frac{17,520 \text{ staff-hours/year}}{1,763.2 \text{ hours/year per staff}} \approx 9.94$$

Since you cannot have a fraction of a staff member, you need to round up to ensure coverage. Therefore, the business will need **10 staff members**.

Thus, the business will need a minimum of 10 staff members to operate 24/7, 365 days a year, with two staff members on duty at all times, accounting for breaks and holidays.

Question Author

Great, thanks

The entitlement to twenty-eight days' annual leave can be in addition to or inclusive of bank holidays so has that been decided yet?

And will public holidays attract an enhanced rate for this venture?

and many holidays and sickness and maternity and paternity and bareavment days and compassionate days could be covered with overtime

3 x 8hr shifts in any 24 hours needs 6 people

That would work for 5 days a week (1 person doing 8 hrs comes to 40 hrs (just over your 38 hr working week) so you'll need weekend cover as well so a minimum of 6 more different people to cover both days. We are already up to 12 people with no mention of sickness and leave.

It's not a simple maths question at all.

What allowances for breaks will they each have?

Just to throw a spanner in the works, from the question it seems we have to ignore 366 day leap years! Even so, that is 52 weeks + 1 day, each worker will therefore work 1981.43 hours (not 1,976) less of course holidays etc.

If breaks are covered by colleagues and an hour is allowed each day, they are covering eighteen hours between them (nine hours each) and not sixteen hours (eight hours each.)

If the working week is thirty-eight hours, that is not eight hours a day and it might not make a difference to a rounded-up calculation but then again, it might.

Where is Typo Typo Typo, the fount of all knowldge on here? I would have thought that would have seen the answer to 20 decimal places!

Un-hypothetically, if you think the cost of running a business is just the salary of the employed staff, you are very much deluded.

Even for a business with minimal overhead costs, multiply that figure by 2 or 3 to be nearer the mark.

Question Author

All the other costs are relatively easy to calculate and have already been factored in, thanks.

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