# Stupid problem I can't solve

1. Jun 16, 2009

### Jeremy111

Hi all,

I am experiencing some problems in solving this simple problem regarding optimization. Here it is:

A fitness center charges $500 for each registration per group of 20 people. The cost will diminish by$5 every time a new member registers. For example, if the group is now formed of 21 people, the cost of each registration will then be $495. I know it is not that hard, but I don't get the idea behind the group of 20 people where each additional member diminishes the cost of each registration. I need to find the maximum revenue, but how can you write this equation in the first place? Thanks! Jeremy 2. Jun 17, 2009 ### fatra2 Hi there, You need to lay down some equation that explains the problem, and then it is quite simple to solve. From 0 to 20, you charge $$500\ \times x$$. For a group bigger than 20, you charge $$[500\ - 5(x-20)]x$$. I believe I help you enough here. You should be able to do the rest. Cheers Last edited by a moderator: Jun 26, 2009 3. Jun 17, 2009 ### FedEx There seems to be a prob with the latex.... Anyways you could differentiate the following and then equal it to zero to get the max revenue.... Number of people = 20 + x Wage for each guy if there are 20+X peolpe = 500 - 50x Hence diff (20+x)(500-5x) 4. Jun 17, 2009 ### Borek ### Staff: Mentor I don't get it, perhaps my English fails me. The more people registers, the higher the revenue, as long as they pay (at some moment registration becomes$0). So to calculate maximum revenue you just need to calculate which is the last person paying.

If you need max revenue per person - as long as there is no more than 20 people registered, it doesn't matter how many people there is.

Both cases are completely unrealistic, but we have to deal with the data as given.

Something doesn't click.

5. Jun 17, 2009

Why 100? If x= 30, there would be 10 "additional members" and the cost per person would be 50- 5(10)= $0. Presumably this problem is predicated on there being at most a few more than 20 people in the group. 11. Jun 26, 2009 ### cristo Staff Emeritus$ is a special latex character, hence to print '$' one needs to write '\$'

12. Jun 26, 2009

### Дьявол

Halls of Ivy, I think you got some error in the equation. Check my post above yours.

Jeremy111 said that the cost for each client is 500$(for <20), and y=500-5*(x-20)=600-5x=5(120-x) for x>20 The cost will diminish by$5 every time a new member registers.

Plug x=21 you will get y=495$, x=22, y=490$... etc...

So the total sum of registrations is the number of members x * the number of individual cost

or

x*(5(120-x))=5x(120-x)

Regards.

13. Jun 26, 2009

### Staff: Mentor

I think didihurt refers to the fact that we are not told what happens when number of people registering is high - are they really get paid then? Seem like registration fee is negative.

14. Jun 26, 2009

### Дьявол

Yes, that's true. The maximum number of members is 120 until the fee reaches 0\$.