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Business applications

  1. Jan 14, 2012 #1

    nyr

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    Okay so I need help with 2 problems. One I did a bunch of work for but im not sure if my answers right, and the second I'm not sure how to start it.
    The first problem:

    A real estate office handles 50 apartment units. When the rent is $720 per month, all units are occupied. However, on average, for each $40 increase in rent, one unit becomes vacant. Each occupied unit requires an average of $48 per month for services and repairs. what rent should be charged to obtain the maximum profit.


    My work:

    I set up an equation
    R= (50-x)(720+40x)-48(50-x)
    R'=1328-80x
    critical number at x=16.6

    50-16.6=33.4
    R(16.6)/33.4=1336
    $1336 should be charged to obtain the maximum profit.

    ------------------------------------------------------

    The second problem:
    When a wholesaler sold a certain product at $25 per unit, sales were 800 units per week. After a price increase of $5, the average number of units sold dropped to 775 per week. Assume that the demand function is linear and find the price that will maximize the total revenue.

    I have no idea how to set up this problem
     
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