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anonymous
 5 years ago
A real estate office manages 50 apartments in a downtown building. When the rent is $900 per month, all the units are occupied. For every $25 increase in rent, one unit becomes vacant. On average, all units require $75 in maintenance and repairs each month. How much rent should the real estate office charge to maximize profits?
P(x) = R(x)  C(x)
This question I am stuck. I don't know how I would formulate the equations for revenue and cost. :
anonymous
 5 years ago
A real estate office manages 50 apartments in a downtown building. When the rent is $900 per month, all the units are occupied. For every $25 increase in rent, one unit becomes vacant. On average, all units require $75 in maintenance and repairs each month. How much rent should the real estate office charge to maximize profits? P(x) = R(x)  C(x) This question I am stuck. I don't know how I would formulate the equations for revenue and cost. :

This Question is Closed

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.050(75) are the costs....$3750

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0or is that only 75 per unit rented?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the rate of change is linear.... 900,50 925,49..... for every 25 over we drop by 1 50=900/25+b 5=90/25+b b = 5  90/25 = 7/5 rooms = cost/25 +(7/5) ??

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0900,50; and 925,49 50 + 900/25 = b lol i forgot to negate the slope

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.050+36 = 86 y = x/25+86

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0that is our demand function;.....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0which can be rewritten as: D(x) = (2150x)/25

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0R * D(x) = total revenue and that has to be at least equal to 3750 to break even right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0since R is the rent charged and x = rent in our demand function; lets do this.. x(2150x)  >= 3750 25

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.02150x  x^2 >= 93750 0 >= x^2 2150x + 93750 +2150/2 is the x amount at the max :) 1075 = x

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0lets see if that amount works out....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.021501075  = rooms rented 25 2150 1075  1075/25 = 43 43(1075)>= 3750 1045 43  4180 3135  $44935 >= 3750...well, we make a profit at least :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.044935 3750  41185 in profits

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we can trey that with 25 higher and 25 lower to see if we are right lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.021501100  = rooms rented 25 2150 1100  1050/25 = 42 ...really? i had to figure it out that way lol...im an idiot :) of course 25 higher is one less lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.01100 42  4400 2200  46200 ......................... see? 1050 44  4200 4200  46200

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0DOH!!...now wheres my mistake lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.01075 43  4300 3225  46225 ...thats better lol, i forgot how to multiply
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