[roxyluv06]

the question is:

A landlord owns an apaertment building. When the rent for each apartment is $700 per month, all 100 apartments are rented. The landlord estimates that each $100 increase in the monthly rent will result in 10 apartments becoming vacant with no chance of being rented. What monthly rent amount will maximize the total monthly revenue?

[ebaines]

I'll help get you started. The total revenue the landlord makes is:

Rev = (No. of apts rented) * (monthly rent rate).

So you need to determine a formula for the No. of apts rented, which you are told is dependent on the monthly rent rate. You're given enough data to construct an equation for the number of apartments rented (call it 'y') given the rent rate ('x') - it will be of the form:

y = Mx + b

where M is the slope of the line, and b is the y intercept. You can find the values for M and b from the data you've been given. Once you have that, then you can use this in the equation for the total revenue, and you'll find it's a quadratic. If you are studying calculus: find where that quadratic is max (i.e. the slope is zero and the 2nd derivative is negative). If you're not that far along yet, just plot the equation for total rev and you'll get it.

Post back and let us know how you are getting along with this.

[Unknown008]

You have to work out some equation for the rent value and the number of corresponding rented apartments.

When the rent is $700, all 100 apartments are rented.
When you increase the rent by $100, that is $800, you'll have 10 less apartments, that is 90.
When you have increased the rent by $200, that is $900, you'll have 20 less apartments, that is 80.
and so on.

Plot these on graph paper, taking the amount of money as the y value and the number of rented apartments as the x value and join the points. Now, have the line y=x drawn. The intersection between the two lines will give the point where the maximum profit is obtained.

Hope it helped! :)

EDIT: oops, sorry ebaines, didn't know you were posting... :o

[antalu1307]

The profit function and the average cost function for a company manufacturing computers are P(x)=396x-2.2x-400 and (c(x))=0.2x+4+400/x respectively where s no. of cmputr manfcturd and sld.Find
I) the total cos function
ii)the total revenue function
iii)maximum revenue
iv)the increase in cost if the number of computer increases from 100 units to 120 units.

[antalu1307]

Sorry... wrong post...

[Unknown008]

Okay, thread closed.