# Thread: Is this Optimization function right?

1. ## Is this Optimization function right?

A real estate developer is contemplating the construction of a luxury condominium building.
Profit per unit is expected to be $200,000 if 20 units are built, but will decrease by$4000 for
each additional unit built on the site. How many units should be built in order to maximize

total profit?

For some reason i find these problems very tricky. So, is this function right for profit?:

Price per unit = 200000 - ((x-20) 4000)

Profit = x(200000 - ((x-20) 4000))

Thanks!

2. Originally Posted by Arturo_026
A real estate developer is contemplating the construction of a luxury condominium building.
Profit per unit is expected to be $200,000 if 20 units are built, but will decrease by$4000 for
each additional unit built on the site. How many units should be built in order to maximize
total profit?

For some reason i find these problems very tricky. So, is this function right for profit?:

Price per unit = 200000 - ((x-20) 4000)

Profit = x(200000 - ((x-20) 4000))

Thanks!
Let N be the number of units more than 20 so

$\displaystyle N = 20 + x$

The profit decreases $4000 per unit so$\displaystyle
P = 200,000 - 4000 x

$Total profit$\displaystyle
PN = (x+20)(200,000-4000x).
$It's this you want to maximize. 3. Originally Posted by Danny The profit decreases$4000 per unit so

$\displaystyle P = 200,000 - 4000 x$
This is what I don't get. The problem says that the price decreases for additional units. So, when 20 units are built the profit is 200,000 and when it's 21, the profit is 196,000. So shouldn't the profit per unit be
$\displaystyle 200,000 - 4,000 (20-x)$

4. Originally Posted by Arturo_026
This is what I don't get. The problem says that the price decreases for additional units. So, when 20 units are built the profit is 200,000 and when it's 21, the profit is 196,000. So shouldn't the profit per unit be
$\displaystyle 200,000 - 4,000 (20-x)$
My numbers are more than 20 whereas yours are starting a zero although if you put in 21 into your formula it gives 204,000 instead of 196,000.

5. Originally Posted by Danny
My numbers are more than 20 whereas yours are starting a zero although if you put in 21 into your formula it gives 204,000 instead of 196,000.
Yes, I meant x-20.
Ok I see, thanks.