1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Triss [41]
2 years ago
7

A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate off

ered to a buyer, the number of sets sold will increase by 210 per week. (a) Find the function representing the demand p(x)p(x), where xx is the number of the television sets sold per week and p(x)p(x) is the corresponding price. p(x)
Mathematics
1 answer:
GuDViN [60]2 years ago
6 0

Correct question is;

A manufacturer has been selling 1400 television sets a week at $450 each. A market survey indicates that for each $21 rebate offered to a buyer, the number of sets sold will increase by 210 per week

A) Find the demand function (price p as a function of units sold x).

p(x)=______

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

$=_____

Answer:

A) p(x) = (-1/10)x + 590

B) Rebate = $170

Step-by-step explanation:

A) We are told that p(x) is the demand function and x is the number of TV sets sold per week.

Now, since for each $21 rebate offered, the number of sets sold increases by 210 per week, it means that the slope here of this demand function is; m = -21/210 = -1/10

Now, he has been selling 1400 TV sets a week at $450 each. This means; p(1400) = $450

Thus, the demand function will be;

p(x) - 450 = (-1/10)(x - 1400)

Expanding the RHS;

p(x) - 450 = (-1/10)x + 140

Add 450 to both sides to get;

p(x) = (-1/10)x + 140 + 450

p(x) = (-1/10)x + 590

B) Formula for revenue is;

R = price × quantity sold

Our demand function is p = (-1/10)x + 590

Making x the subject, we have;

x = 5900 - 10p

x is quantity sold.

Thus,

R = p(5900 - 10p)

R = 5900p - 10p²

Maximum price will occur at dR/dP = 0

Thus;

dR/dP = 5900 - 20p

At dR/dP = 0,we have;

20p = 5900

p = 5900/20

p = $280

Thus, rebate = 450 - 280 = $170

You might be interested in
<img src="https://tex.z-dn.net/?f=1%20%5Cdiv%201%20%2B%20a%20%20%7Bl%7D%20-%20%7Bm%7D%20%20%2B%201%20%5Cdiv%201%20%2B%20%20%7Bm%
ziro4ka [17]

Answer:

Using BODMAS

first solve division, then go for addition or subtraction

1 \div 1 + al - m + 1 \div 1 + m - l\\ =(1 \div 1) + al - m +( 1 \div 1) + m - l\\ =1 + al - m + 1 + m - l\\ = 2 + al -l\\=2 + l(a - 1)

6 0
3 years ago
What properties cannot be used in a proof
forsale [732]
I am certain the answer is C. Algebra properties are used in proofs. Postulates are definitely used. And definitions are explanations. So, it is C.
5 0
3 years ago
7x-7+35-34p+(45x-2p)+6^4
ss7ja [257]

Answer:

=−36p+52x+1324

Step-by-step explanation:

7x−7+35−34p+45x−2p+64

=7x+−7+35+−34p+45x+−2p+1296

Combine Like Terms:

=7x+−7+35+−34p+45x+−2p+1296

=(−34p+−2p)+(7x+45x)+(−7+35+1296)

=−36p+52x+1324

6 0
3 years ago
Read 2 more answers
What is the value of v? v/-8=v 4?
Ray Of Light [21]
V/-8 = 4v
V= -32v
V+32v=0
33v=0
V=0
8 0
3 years ago
Read 2 more answers
Which of the following is the mid point of the line segment with endpoints -3 and 2 (a)5/2 (b) 1 (c) -1/2 (d) -1 (e)-5/2
scoray [572]

Answer:

2,5 b 1 c 0,5 d -1 e 2,5

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • NEED HELP STAT WHATS 9+10
    13·2 answers
  • River raft rentals are 7$ per hour plus a deposit fee of $25 per person. Write an expression for the total cost of renting a raf
    8·2 answers
  • Help??!?! I honestly forgot
    7·2 answers
  • The value of a piece of jewelry bought new for $2,200 decreases 12% each year. Use a graph to predict the value of the jewelry i
    14·1 answer
  • Find the difference between 24 1/8 minus 6 3/4
    12·2 answers
  • Lloyd's Cereal company packages cereal in 1 pound boxes (16 ounces). A sample of 16 boxes is selected at random from the product
    11·1 answer
  • Name a combination of 12 coins that equals 3 dollars (has to be dimes &amp; quarters)
    8·1 answer
  • Please answer this to the best of your ability
    15·1 answer
  • Please Help Me! Find the missing length indicated. Leave your answer in simplest radical form.
    12·1 answer
  • Oh so you like Friday night funkin then name every song G
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!