## luijie 3 years ago can you answer this? Fil-invest realty handles a condominium of 100 units. Their experience shows that if the rent for each unit is P10,000/month all of the units will be occupied, but 10 units will become vacant for each P1,000 increase in monthly rate. what rate should be charged to maximize the total revenue? use second derivative test.

1. 14yamaka

I think the equation looks like this: f(x)=(10000+1000x)(100-10x) x= the number of increases in 1000's

2. 14yamaka

But...the answer that comes out with this is really weird So, if this is multiplied out, we get 1,000,000-100,000x+100,000x-10000x^2 =1,000,000-10000x^2 Then, taking the first derivative, dy/dx=-20000x d^2y/dx^2=-20,000

3. vishal_kothari

it is tough..give me some time...

4. 14yamaka

Thank you!

5. vishal_kothari

for what?

6. 14yamaka

ahh....helping out on this question i think?

7. shaan_iitk

@14yamaka .. actually it makes sense that in order to maximize your revenue you would not increase the cost per unit .. why ?? because each unit is giving you 10000 per month .. while an increase of even 1000 per unit would make you loose 10 units .. that is 10000*10 (minimum loss) which is way more than what you would gain by increasing the cost.. I think the question possibly is wrong or some value is given incorrectly...

8. 14yamaka

oh...yeah, I wondered if it wasnt already maximum, but it said to use the second derivative so i did...that's a good conclusion though :)