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
Korvikt [17]
3 years ago
15

A bakery works out a demand function for its chocolate chip cookies and finds it to be q = D (x) = 943 - 17 x​, where q is the q

uantity of cookies sold when the price per​ cookie, in​ cents, is x.
A) Find the elasticity.
B) At what price is the elasticity of demand equal to 1?
C) At what prices is the elasticity of demand elastic?
D) At what prices is the elasticity of demand inelastic?
E) At what price is the revenue a maximum?
F) At a price of 21c per cookie, will a small increase in price cause the total revenue to increase or decrease?
1. Increase
2. Decrease
Mathematics
1 answer:
Alex73 [517]3 years ago
5 0

Answer:

See expla below

Step-by-step explanation:

Given the demand function:

q = D (x) = 943 - 17 x

a) Find the elasticity:

Find the derivative of the demand function.

D'(x)= -17

Thus, elasticity expression is:

\frac{x D'(x)}{D'(x)}

= \frac{x (-17)}{943 - 17x}

= \frac{17x}{943 - 17x}

Elasticity expression = E(x) = \frac{17x}{943 - 17x}

b) At what price is the elasticity of demand equal to 1?

This means E(x) = 1

Substitute 1 for E(x) in the elasticity equation:

E(x) = \frac{17x}{943 - 17x}

1 = \frac{17x}{943 - 17x}

Cross multiply:

943 - 17x = 17x

Collect like terms

17x + 17x = 943

34x = 943

x = \frac{943}{34}

x = 27.74

Elasticity at the price of demand = 1 is 27.74

c) At what prices is the elasticity of demand elastic?

This means E(x) > 1

Therefore,

\frac{17x}{943 - 17x} > 1

\frac{17x}{943 - 17x} > 1

Cross multiply:

17x > 943 - 17x

Collect like terms

17x + 17x > 943

34x > 943

x > \frac{943}{34}

x > 27.74

The elasticity of demand is elastic at x > 27.74

d) At what prices is the elasticity of demand inelastic?

This means E(x) < 1

Therefore,

\frac{17x}{943 - 17x} < 1

\frac{17x}{943 - 17x} < 1

Cross multiply:

17x < 943 - 17x

Collect like terms

17x + 17x < 943

34x < 943

x < \frac{943}{34}

x < 27.74

The elasticity of demand is inelastic at x < 27.74

e) At what price is the revenue a maximum:

Total  revenue will be:

R(x) = x D(x)

= x (943 - 17x)

= 943x - 17x²

R(x) = 934 - 17x(price that maximizes total revenue)

Take R(x) = 0

Thus,

0 = 943 - 17x

17x = 943x

x = \frac{943}{17}

x = 27.74

Total revenue is maximun at x= 27.74 per cookie

f) At x = 21 per cookie, find the price:

Thus,

R (21) = (943 * 21) - (17 * 21²)

= 19803 - 7497

= 12306

At x = 27.74, find the price:

R(27.74) = (943 * 27.74) - (17 - 27.74²)

= 26158.82 - 13081.63

= 13077.19

We can see the new price of cookie causes the total revenue to decrease.

Therefore, with a small increase in price the total revenue will decrease.

You might be interested in
Hello can u help plz?
I am Lyosha [343]

Answer:

slope would be 3 or 3/1

Step-by-step explanation:

I think i'm not totally sure it could be -3 or -3/1

7 0
2 years ago
The length of a rectangle is five times its width.
kykrilka [37]

Answer:

w=10

L=50

Step-by-step explanation:

<h2><em>Length=5w</em></h2><h2><em>Width=W</em></h2>

6w=60

----   ----

6       6

w=10

5(10)=50

L=50

Also can you make me the top answer?

4 0
3 years ago
24 students in a class took an algebra test <br><br> If 18 students passed what percent passed
Anuta_ua [19.1K]

Answer: 75%

We know that 1/4 of 24 (25%) is 6, 6 fits into 18 three times and 25 times 3 is 75. So the answer is 75%

6 0
2 years ago
Selecting an Instructor At a convention there are 7 mathematics instructors, 5 computer science instructors, 3 statistics instru
LiRa [457]

Answer:

11/19

Step-by-step explanation:

Firstly, we need to know the total number of instructors. This is equal to 7+5+4+3 = 19 instructors.

The probability of selecting a science instructor is 4/19

The probability of selecting a math instructor is 7/19

The probability of selecting either a science or a maths instructor is 4/19 + 7/19 = 11/19

4 0
3 years ago
How many cylindrical can of bottles 12 cm high and with 6 cm diameter could be filled from a tank containing 125 liters of deter
Orlov [11]

Answer:

368 cans.

Step-by-step explanation:

Volume of 1 can = π r^2 h.

Here h (height) = 12 and r (radius) = 1/2 * 6 = 3 cm.

So V =  π * 3^2 * 12

= 108π cm^3.

The tank hold 125 liters

=  125,000 cm^3, so:

Number of cans that could be filled = 125000/ 108 π

= 368.4.

4 0
3 years ago
Read 2 more answers
Other questions:
  • Help please tia everyone!
    14·1 answer
  • Including a 6% sales​ tax, an inn charges $265 per night. Find the​ inn's nightly cost before the tax is added
    8·2 answers
  • Help pleaseeeeeeeeeeeee!
    10·1 answer
  • A community needs to raise at least 5,000
    6·1 answer
  • If gross pay increases by $500, total employee benefits increase by $200 and total job expenses decrease by $300, then total emp
    8·2 answers
  • Pls help me. I will mark you as brainly if you help me get the correct answer.
    8·2 answers
  • SIZE A ranch in Wyoming is
    10·1 answer
  • Please answer this questions ​
    15·1 answer
  • I need help understanding this ASAP plz, I have a quiz over this next week!!!!
    7·1 answer
  • Kiran's mother gets a restaurant bill for $25. She has a coupon for 15%. After the discount is applied, she adds 20% as a tip. W
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!