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 (110x+1000)(480−11x). Which is marked correct b) 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 levels c) 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?

easternerjx

easternerjx

Answered question

2022-09-24

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 (110x+1000)(480−11x). Which is marked correct
b) 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 levels
c) 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?

Answer & Explanation

nutnhonyl8

nutnhonyl8

Beginner2022-09-25Added 8 answers

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 17.2
The rebate offered must therefore be
$ 17.2 11 = $ 190 dollars

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