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

Kaiden Wilkins 2022-05-07 Answered

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 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)

overnachtt9xyx

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 \Leftrightarrow - 2420 x + 41800 \Leftrightarrow x \approx 17.2

The rebate offered must therefore be

$ 17.2 \cdot 11 = $ 190 dollars

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