Maximizing Output in a Factory: Finding the Optimal Number of Employees

[khopcraft]

The question I have received is this:
There are 50 employees in a factory. Each person produces 800 sticky notes. For each additional worker hired by the factory, the output per person drops by 10 sticky notes. How many people should be hired by the company in order to maximize the total output of workers?
(Hint: create an equation for output or production)

Basically, I am stuck with getting the equation for output. I can get an equation that works, but I don't think it will help me solve the rest of the problem. I got this equation:
f(x)=(800 - (x-50)(10))(x)
where x is the number of employees.

If I do this, I can get the total output, but I don't think I can find the maximum efficiency without plugging in numbers many times over, till I find the one that is the maximum.

So can someone help me get the proper equation? Or if that is the proper equation, could I please be pushed in the right direction as what to do next?

 

[tiny-tim]

welcome to pf!

hi khopcraft! welcome to pf!

f(x)=(800 - (x-50)(10))(x)
where x is the number of employees.

that looks fine

it's a quadratic equation , so to maximise it either use calculus or complete the square

 

[khopcraft]

Hi, thanks for the welcome, and the quick reply. I am a little confused as to how to use the quadratic formula with this, as there are no squared variables and such.

Sorry, its been a while since I have done this.

 

[tiny-tim]

f(x)=(800 - (x-50)(10))(x)

= (1300 - x)x

= 1300x - x²

 

[khopcraft]

Ouch, it was simple mathematics. Thanks a ton. You sir, are awesome.