anonymous
  • anonymous
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. :|
Mathematics
schrodinger
  • schrodinger
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amistre64
  • amistre64
50(75) are the costs....$3750
amistre64
  • amistre64
or is that only 75 per unit rented?
amistre64
  • amistre64
the 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) ??

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amistre64
  • amistre64
900,50; and 925,49 50 + 900/25 = b lol i forgot to negate the slope
amistre64
  • amistre64
50+36 = 86 y = -x/25+86
amistre64
  • amistre64
that is our demand function;.....
amistre64
  • amistre64
which can be rewritten as: D(x) = (2150-x)/25
amistre64
  • amistre64
R * D(x) = total revenue and that has to be at least equal to 3750 to break even right?
amistre64
  • amistre64
since R is the rent charged and x = rent in our demand function; lets do this.. x(2150-x) --------- >= 3750 25
amistre64
  • amistre64
2150x - x^2 >= 93750 0 >= x^2 -2150x + 93750 +2150/2 is the x amount at the max :) 1075 = x
amistre64
  • amistre64
lets see if that amount works out....
amistre64
  • amistre64
2150-1075 ---------- = 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
  • amistre64
44935 3750 ------ 41185 in profits
amistre64
  • amistre64
we can trey that with 25 higher and 25 lower to see if we are right lol
amistre64
  • amistre64
2150-1100 ---------- = 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
  • amistre64
1100 42 ----- 4400 2200 ------- 46200 ......................... see? 1050 44 ----- 4200 4200 ------ 46200
amistre64
  • amistre64
DOH!!...now wheres my mistake lol
amistre64
  • amistre64
1075 43 ----- 4300 3225 ------ 46225 ...thats better lol, i forgot how to multiply

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