math

posted by nhokaishiteru

miss Thao owns a small hotel with 30 identical rooms. she finds that if she charges a price of 12 dollars ( or less) per room per day, all the rooms are rented. for every 1 dollar in price, 2 rooms remain vacant. each day, maintenance cost 4 dollars per rented room and 1 for unrented room. what price should miss thao charge n order to maximize her daily profit? hint: profit = revenue - costs
Help me, thanks a lots

  1. Reiny

    current number of rooms = 30
    current price per room = 12

    let the number of additional increases of $1 be n

    numbers of rooms rented = 30 - 2n
    number of rooms not rented = 30 - (30-2n) = 2n
    price per room = 12 + n

    Profit = (12+n)(30-2n) - 4(30-n) - 1(2n)
    = 360 + 6n -2n^2 - 120 + 4n - 2n
    = -2n^2 + 8n + 240

    by Calculus:
    d(profit)/dn = -4n + 8
    = 0 for a max of profit
    4n = 8
    n = 2

    the price per room should be 12+n = 12+2
    = $ 14.00

    if you don't know calculus:

    profit = -2n^2 + 8n + 240
    the n of the vertex = -8/-4 = 2
    so the price should be $ 14.0

  2. nhokaishiteru

    tks Reiny so much :x

Respond to this Question

First Name

Your Answer

Similar Questions

  1. 12

    The Green Mountain Inn can rent all its 210 rooms when it charges $45 per night for a room, but the manager wants to increase profits. He finds, however, that for each $2 increase in the room rate, 3 fewer rooms are rented. If the …
  2. math

    a hotel chain charges $120 per room and rents an avg of 40 rooms per night at this rate. For each $10 reduction in price, they rent an avg of 10 more rooms. Find the rate they should be charging to maximize revenue. Help please! Thanks!
  3. math

    a hotel chain charges $120 per room and rents an avg of 40 rooms per night at this rate. For each $10 reduction in price, they rent an avg of 10 more rooms. Find the rate they should be charging to maximize revenue. Help please! Thanks!
  4. ALGEBRA

    A nearby resort rented a certain number of function rooms for Php 28,800. When the price was reduced by Php 20 per room, 6 more rooms were rented. How many function rooms were rented?
  5. math

    Help please >.< The Hotel Lakewell has 450 rooms. Currently the hotel is filled . The daily rental is $ 750 per room. For every $ 4 increase in rent the demand for rooms decreases by 7 rooms. Let x = the number of $ 4 increases …
  6. math

    Help pleaseeee The Hotel Regal has 500 rooms. Currently the hotel is filled. The daily rental is $ 400 per room. For every $4 increase in rent the demand for rooms decreases by 8 rooms. Let x be the number of rooms that are being rented …
  7. Math

    The Hotel Regal has 600 rooms. Currently the hotel is filled . The daily rental is $ 250 per room. For every $ 4 increase in rent the demand for rooms decreases by 4 rooms. Let x = the number of $ 4 increases that can be made. What …
  8. pre-calculus

    The Hotel Florence has 550 rooms. Currently the hotel is filled . The daily rental is $ 700 per room. For every $ 14 increase in rent the demand for rooms decreases by 7 rooms. Let x = the number of $ 14 increases that can be made. …
  9. precalculus

    The Hotel Thomasina has 500 rooms. Currently the hotel is filled . The daily rental is $ 1000 per room. For every $ 4 increase in rent the demand for rooms decreases by 8 rooms. Let x = the number of $ 4 increases that can be made. …
  10. College Algebra

    A large hotel finds that it can rent 95 rooms when it charge $100 per room. For each $1 increase in room cost it rents one room less. (Likewise, for each $1 decrease in room cost it rents one room more) What price should it charge …

More Similar Questions