Statement:A manufacturer has been selling 1000 television sets a week at $ 480 each. A market survey indicates that for each $ 11 rebate offered to a buyer, the number of sets sold will increase by 110 per week.Questions :a) Find the function representing the revenue R(x), where x is the number of $ 11 rebates offered.For this, I got ( 110 x + 1000 ) ( 480 − 11 x ). Which is marked correctb) How large rebate should the company offer to a buyer, in order to maximize its revenue?For this I got 17.27. Which was incorrect. I then tried 840999, the sum total revenue at optimized levelsc) If it costs the manufacturer $ 160 for each television set sold and there is a fixed cost of $ 80000, how should the manufacturer set the size of the rebate to maximize its profit?For this, I received an answer of 10, which was incorrect.

Question

Statement:A manufacturer has been selling 1000 television sets a week at   $  480 each. A market survey indicates that for each   $  11 rebate offered to a buyer, the number of sets sold will increase by 110 per week.Questions :a) Find the function representing the revenue R(x), where x is the number of   $  11 rebates offered.For this, I got   (  110  x  +  1000  )  (  480  −  11  x  ). Which is marked correctb) How large rebate should the company offer to a buyer, in order to maximize its revenue?For this I got 17.27. Which was incorrect. I then tried 840999, the sum total revenue at optimized levelsc) If it costs the manufacturer   $  160 for each television set sold and there is a fixed cost of   $  80000, how should the manufacturer set the size of the rebate to maximize its profit?For this, I received an answer of 10, which was incorrect.

overnachtt9xyx · Accepted Answer

For part b, the question is: for what x is   R  (  x  )  =  (  110  x  +  1000  )  (  480  −  11  x  ) maximized?First, differentiate using the power rule and then set the derivative equal to zero:      R    ′    (  x  )  =  110  (  480  −  11  x  )  −  11  (  110  x  +  1000  )  =  −  2420  x  +  41800      R    ′    (  x  )  =  0  ⇔  −  2420  x  +  41800  ⇔  x  ≈  17.2The rebate offered must therefore be  $  17.2  ⋅  11  =  $  190    dollars

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