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Math Help - Demand problem

  1. #1
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    Demand problem

    A manufacture has been selling 1650 tv sets a week at 420 each. A market survey indicates that for each 29 rebate offered to a buyer, the number of sets sold will increase by 290 per week.

    a) Find the demand function p(x), where x is the number of the television sets sold perweek. p(x) =

    b) How large rebate should the company offer to a buyer, in order to maximize its revenue?

    c) If the weekly cost function is 115500 + 140x. How should it set the size of the rebate to maximize its profit?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by tttcomrader View Post
    A manufacture has been selling 1650 tv sets a week at 420 each. A market survey indicates that for each 29 rebate offered to a buyer, the number of sets sold will increase by 290 per week.

    a) Find the demand function p(x), where x is the number of the television sets sold perweek. p(x) =

    b) How large rebate should the company offer to a buyer, in order to maximize its revenue?

    c) If the weekly cost function is 115500 + 140x. How should it set the size of the rebate to maximize its profit?
    A prive reduction of $29 increases sales by 290, so the sales chanve by -10 per $ increase in price. So assume a linear reation between demand and price:

    x=-10 p +c

    where x is the demand, and p the price, then as 1650 are sold at a price of $420 c=5850, and the demand function is:

    x=-10 p + 5850.

    Inverting this we get:

    p(x)=585-0.1x

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by tttcomrader View Post
    A manufacture has been selling 1650 tv sets a week at 420 each. A market survey indicates that for each 29 rebate offered to a buyer, the number of sets sold will increase by 290 per week.

    b) How large rebate should the company offer to a buyer, in order to maximize its revenue?

    c) If the weekly cost function is 115500 + 140x. How should it set the size of the rebate to maximize its profit?
    Revenue is:

    r=x p(x)

    maximise this to find the price/sales that maximise revenue, and then calculate the corresponding discount.

    Profit is:

    prft(x) = r - costs =x p(x) - (115500 + 140x)

    Now proceed as before

    RonL
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