A few months ago we celebrated our son's Bar Mitzvah party. This was the first large-scale formal celebration that was held not in our back yard (unlike our wedding and a few other big bashes we have had). And the food was not the usual potluck or Trader Joe's or grilled meat, but a pre-tasted catering selection. I spent a month picking a place with nice vibe, good views, reasonable food and price, and plentiful parking space. And, by the way, the place was half-a-way across the globe, in Israel, where most of our family and quite a few friends live. We celebrated in Tel Aviv, on the banks of the Yarkon river, in the restaurant space of the Daniel Amihai Rowing center, which looked magnificent in the evening and had even better views from inside, of the city skyline and Mediterranean sunset.

About a week before the event we had to provide the exact head count. We were told that this would be the minimum amount of people we will pay for. Even if only half of these guests will show up, we will have to pay for the ordered amount as the chef will prepare the food for that amount. Should a few extra guests pop up, we will pay for each of their portions as well, on top of the agreed upon amount. Inexperienced in such situations and dealing with relatives that we haven't seen in a while and customs we are no longer used to, we were not sure how exactly to estimate the expected head count most precisely. We invited 120, but how many will show up? The answer seemed to lay somewhere between 70 and 125.

Price-per-person depended on the number of people we reserve for:

less than 100 guests - $80 each

more than 100 guests - $64 each

in addition to the price-per-person, there was a service fee:

$100 for each waiter that serves 10 people

the more people will show up, the more waiters we would need

We tried to call and email everyone (no RSVP customs in Israel) carefully inquiring who is coming, but then we realized that some mathematical thinking and less precision could save us some money and time. How?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

About a week before the event we had to provide the exact head count. We were told that this would be the minimum amount of people we will pay for. Even if only half of these guests will show up, we will have to pay for the ordered amount as the chef will prepare the food for that amount. Should a few extra guests pop up, we will pay for each of their portions as well, on top of the agreed upon amount. Inexperienced in such situations and dealing with relatives that we haven't seen in a while and customs we are no longer used to, we were not sure how exactly to estimate the expected head count most precisely. We invited 120, but how many will show up? The answer seemed to lay somewhere between 70 and 125.

Price-per-person depended on the number of people we reserve for:

less than 100 guests - $80 each

more than 100 guests - $64 each

in addition to the price-per-person, there was a service fee:

$100 for each waiter that serves 10 people

the more people will show up, the more waiters we would need

We tried to call and email everyone (no RSVP customs in Israel) carefully inquiring who is coming, but then we realized that some mathematical thinking and less precision could save us some money and time. How?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

## 5 comments:

TracyZ answer:

There are two categories of costs in this problem:

1) The costs related to the food and drink itself

These costs vary by the number of people that the caterer is told will be attending, plus any extra people who show up on the day of the event ($80 or $64 per person).

2) The costs related to the waiter service provided at the meal. These costs are a function of the number of people who actually attend the event ($100 fee for each 10 people).

Because the #2 costs are completely determined on the day on the event, I did not consider them for the posted problem, which asks how many people the caterers should be told to expect for dinner, the answer for which relates to the #1 costs.

The problem states the food/drink cost as:

$80 per person for less than 100 people and

$64 per person for more than 100 people

and indicates that the caterer can accompany a few extra people more than the reservation on the day of the event.

The problem left me with a few questions:

A) what is the cost of the food/drink for precisely $100 people, and

B) how many extra people can be accommodated without advance reservation on the day of the event, in other words, how is a "few" defined.

For the problem we are told that the number of guests will range from 70 to 125. The midpoint of these two numbers is 97.5, which is close to 100.

If the per person food/drink price drops at 100 guests, and if the caterer can accommodate up to 20+ extra guests on the day of the event, then I might give the caterer a headcount of 100. Because of the volume discount, the total food/drink price for 100 guests is the same cost as for 80 guests ($6400). Over 100 guests, the hosts would pay $64/person for any extra guests on the day of the event.

If the caterer can accommodate fewer extra guests over the pre-event headcount (say 10-15) on the day of the event, then I might give the caterer a head count of 110, just in case since I want there to be enough food for all. The total food/drink price for 110 guests is the same cost as for 88 guests ($7040).

I don't know how caterered events work in Israel, but in the US, it seems to me as though caterers typically overestimate how much food people will eat and there are often lots of leftovers, even when the number of guests in attendance is very close to the pre-event headcount. If it's like that in Israel as well, that might influence my thinking. At the same time, given all the planning and expense of the event, and going to Israel for it, I wouldn't want to give the caterer an advanced headcount that I thought was likely to be too small, just to save a little bit of money. (Hopefully, that wouldn't be the case with a headcount of 100 or 110). I’d take these sorts of factors, and factors such as how many RSVPs I had received and how many people were definitely likely to attend, into account in creating the pre-event headcount.

One last thought: in case the number of actual guests at the event turns out to be less than the pre-event headcount, I’d want to want to make advanced arrangements regarding what would happen with the extra food so that it wouldn’t go to waste. Again, I don’t know how this circumstance is typically handled in Israel.

You have to make three assumptions.

1. I had to decide what to do about 100 guests. I assumed that the breaking point for 100 dollars a plate was 99. After 99, the break of 64 dollars a plate kicks in.

2. I wasn't sure what to do about several. I took it to mean 10. That meant that you would need 1 extra waiter and 640 dollars extra payment for over the top guests.

3. I assumed that if the guest list went so much as 1 over a zero number, another waiter was needed.

Let's see what happens with these assumptions.

The cost for 70 guests = 8800 dollars. It breaks down like this

70 guests = 7000

7 waiters = 700

10 extras = 1000

1 waiter = 100

Total = 8800.

100 guests = 6400

10 waiters = 1000

10 extras = 640

1 waiter = 100

Total = 8140

This is much much lower. Now you might want to consider what happens after 100. 101 for example, comes to 8304

Every other number will go up from there. I would say you have no control over what happens if the number goes much higher, but it is still better to pay for more plates then less.

Anything under 100 guests, pay for 100. Over 100, you have a problem.

Sorry to make so many entries. I misread the givens.

Up to 78 people and retaining my assumptions, you are better off paying for the number of guests you think are coming plus 10 extrea.

After 78 but less than 100 you are much better off paying for 100. After 100, you have to go with the guess.

The method of calculation is the same as outlined in one of my previous answers.

I found it pretty amazing that one can pay less for more people. If I would reserve for 90 people, I will have to pay:

90 x $80 = $7,200

9 x $100 = $900

$8,100 total

However if I will reserve for 100, it will be:

100 x $63 = $6,300

10 x $100 = $1,000

$7,300 total

We ended up using the 100 number and to be honest I don't even know how many people showed up - somewhere very close to the 100. This, by the way, was considered to be a small party in Israel:)

Thank you - Tracy and Jerome for the thorough answers. I am surprised the others stay shy, probably the question was too long.

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