After collecting an advance rental fee of $50 and providing an appropriate list of rentals, you are unable to provide your client with a rental she likes. She requests a refund upon the expiration of your agreement. You must return ? A nothing if you provided a list of at least three rentals. ? B $50. C $25.
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Challenge #10: room rental C Let's once more return to Challenge #3 and the extra room you have to rent nightly. You have decided to turn it over to a property management company that offers the following options. Option 1 Limited work required by you. You must update the listing, the rental company handles the rest (e.g., reservations, payment, cleaning). This option has the cost function C(x) = 120 + 24x +.02x² and the price or demand function D(x) = -.8x + 58. Option 2 No work required by you. This option has the cost function C(x) = 120 + 30x +.04x² and the price or demand function D(x) = -.6x + 62. Option 3 No work required by you plus green cleaning. This is the same as Option 2 except the rental company uses a green cleaning service. This option has the cost function C(x) = 120 + 40x +.06x² and the price or demand function D(x) = -.7x + 76. For each option: a. Determine how many nights your room needs to be rented in a month to maximize your profit. Prove that this value is a maximum. b. Determine your maximum monthly profit. Based on these calculations, which option should you choose? What non-mathematical factors might affect your decision?
Supreeta N.
The owner of an apartment building can rent all 50 apartments if she charges $1,800 per month, but she rents one fewer apartment for each $60 increase in monthly rent. (a) Construct a table that gives the revenue generated if she charges $1,800, $1,860, and $1,920. (b) Does her revenue from apartment rentals increase or decrease as she increases the rent from $1,800 to $1,920? (c) Write an equation that gives the revenue R, from apartment rentals if she makes x increases of $60 in the rent. (d) Find the rent she should charge to maximize her revenue.
The Case of Left Holding the Lease Erica has a problem. She and her friend Shira found a two-bedroom apartment to share, only Erica signed the lease. Consequently, Erica is legally responsible for fulfilling the terms of the lease. In the spring of her first year of college, they paid the security deposit on the apartment. However, now, only two weeks before the start of the fall term, Shira has told Erica that she can't afford the rent and has decided to live with her parents. Erica is simultaneously furious with Shira and panicky at the thought of having to pay the rent by herself. How is she going to deal with the problem?
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