Statement: A manufacturer has been selling 1000 television sets a week at <mi mathvariant="n

Kaiden Wilkins 2022-05-07 Answered

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 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?

For this, I received an answer of 10, which was incorrect.
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Answers (1)

Answered 2022-05-08 Author has 10 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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