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 quantity 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
Answers
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.
The demand is elastic when the change in the quantity demanded with
respect to change in price is significant.
\(A) \ \displaystyle \mathrm{Elasticity, \ } \underline{ \epsilon = \displaystyle \frac{17 \cdot x}{943 - 17\cdot x}}\)B) The price at which the elasticity is one is approximately 27.74cC) The elasticity is elastic when the price is larger than 27.74cD) The elasticity is inelastic when the price is lesser than 27.74cE) The revenue is maximum when the price is approximately 27.74cF) 1. IncreasesReasons:
A) The demand function is; q = D(x) = 943 - 17·x
Where;
q = The quantity of cookies sold
x = The price of cookies
Elasticity of demand is given by the formula;
\(\displaystyle \epsilon = \mathbf{\frac{\Delta Q}{\Delta P} \times \frac{P}{Q}}\)
\(\displaystyle \frac{\Delta Q}{\Delta P} = 17\)
\(\displaystyle \frac{P}{Q} = \frac{x}{943 - 17\cdot x}\)
Therefore;
\(\displaystyle \underline{ \mathrm{Elasticity, \ } \epsilon = \displaystyle \frac{17 \cdot x}{943 - 17\cdot x}}\)
B) When the elasticity, ε = 1, we have;
\(\displaystyle \displaystyle \frac{17 \cdot x}{943 - 17\cdot x} = 1\)
943 - 17·x = 17·x
943 = 17·x + 17·x = 34·x
\(\displaystyle x = \frac{943}{34} \approx 27.74\)
When the elasticity, ε = 1, the price, x ≈ 27.74
C) The demand is elastic when, ε > 1, which gives;
\(\displaystyle \displaystyle \epsilon = \frac{17 \cdot x}{943 - 17\cdot x} > 1\)
17·x > 943 - 17·x
\(\displaystyle x > \frac{943}{34}\)
\(\displaystyle \frac{943}{34} \approx 27.74\)
Which gives;
x > 27.74
The price at which the elasticity of demand is elastic is x > 27.74
D) The elasticity of demand is inelastic when we have;
\(\displaystyle \displaystyle \epsilon = \mathbf{ \frac{17 \cdot x}{943 - 17\cdot x} }< 1\)
Which gives;
17·x < 943 - 17·x
17·x + 17·x < 943
34·x < 943
\(\displaystyle x < \frac{943}{34}\)
x < 27.74
E) The total revenue, R = Price × Quantity sold
∴ R = x × 943 - 17·x = 943·x - 17·x²
When the revenue is maximum, we have;
\(\displaystyle R' = 0 = \frac{d}{dx} \left(943 \cdot x - 17 \cdot x^2 \right) = 943 - 34 \cdot x\)
Which gives;
943 - 34·x = 0
943 = 34·x
x ≈ 27.74
When the revenue is maximum, the price, x ≈ 27.74
F) When the price is 21c
The total revenue is given from the revenue formula and the price at maximum revenue as follows;
The function for the total revenue is, R = 943·x - 17·x²
The sign of the leading coefficient is negative, the graph of the total revenue function is concave down and from question e, the price at the maximum revenue, x = 27.74, which gives;
At points before x = 27.74, a small increase in price will cause the total revenue to increase
Therefore, at x = 21c, a small increase in price will cause the total revenue to increase. The correct option is 1. Increase
Learn more here:
https://brainly.com/question/15654343
Related Questions
.......... do it now? Can't I do it later?
a) I've to
b) Have I
c) Do I have to
d) Should I
Answers
Answer:
d
Step-by-step explanation:
You are asking a question trying to suggest whether it can be done later
help me
If x=1/2 and y=2/3 , find the value of xy+ (x+ y)
Answers
Answer:
3/2
Step-by-step explanation:
in which part of the number line would 112% be located?
Answers
Answer:
It would be 1.12 away from 0
Suppose that the demand of a certain item is x=-0.7p+10.
Evaluate the elasticity at 6.
Answers
The item is an inelastic good at a price of 6 because it is negative and have a demand of -0.71.
What is the item's demand if elasticity is at 6?The formula for elasticity of demand is Elasticity of demand = (% change in quantity demanded) / (% change in price)
The initial quantity demanded at a price of 6 and the quantity demanded at a slightly different price must be know.
Let say Initial quantity demanded is:
x = -0.7(6) + 10
x = 5.8
Assume price changes slightly to 6.01, which gives us a new quantity demanded of x:
= -0.7(6.01) + 10
= 5.793
The % change in quantity demanded will be:
= [(new quantity demanded - initial quantity demanded) / initial quantity demanded] x 100%
= [(5.793 - 5.8) / 5.8] x 100%
= -0.12%
As price has changed from 6 to 6.01, we can calculate the percentage change as follows:
% change in price = [(new price - initial price) / initial price] x 100%
= [(6.01 - 6) / 6] x 100%
= 0.17%
Elasticity of demand = (% change in quantity demanded) / (% change in price)
= (-0.12% / 0.17%)
= -0.71
Read more about demand elasticity
brainly.com/question/29615048
#SPJ1
Write an equation in standard form (1,1) (2,5) Ax+By=-3
Answers
The Equation of the Line in Standard form is 4x - y = 3
What is Slope of a Line?
The slope formula is used to compute the inclination or steepness of a line. The slope of the lines is calculated using the x and y coordinates of the lines. It is the ratio of the y-axis change to the x-axis change.
Solution:
Slope of the Line passing through the points (1, 1), (2, 5)
is
m = 5-1/2-1 = 4
Equation of the line = (y - y1) = m(x - x1)
y - 1 = 4(x - 1)
y - 1 = 4x - 4
4x - y = 3
To learn more about Slope of a Line from the given link
https://brainly.com/question/16949303
#SPJ1
i need help with this one
Answers
The value of x from the given figure is 8
How to calculate the interior angle of a triangleA triangle is a 2-dimensional shape with 3 sides an interior angle
Since the sum of the interior angles of a triangle is 180 degrees, hence;
8x - 4 + 76 + 44 = 180
8x + 116 = 180
8x = 180 - 116
8x = 64
x = 64/8
x = 8
Hence the value of x from the given figure is 8
Learn more on interior angle of a triangle here: https://brainly.com/question/8611232
what it
6x8 divide by 5.2x24 divide 7
Answers
I know it’s because of Cymath
Help plz worth 100 points+ Brainliest:))
Answers
Answer:
0.875 or for the short way 0.88
Answer:
Step-by-step explanation:
So 9) would be 0.875, 87.5%
11) would be 0.625, 62.5%
12) would be 0.9, 90%
13) would be 0.35, 35%
14) would be 0.25, 25%
PS:IM TRYING TO GET THAT GRADE UPGRADE
Answers
Using direct variation to find the constant of proportionality which is 27 and they can pay 10 rooms with $256.50
What is Proportional RelationshipProportional relationship is a mathematical concept where two variables are directly proportional to each other, meaning that their ratio remains constant. This can be expressed as an equation y = kx, where k is the constant of proportionality and x and y are the two variables. In this relationship, if x increases, y also increases, and if x decreases, y decreases, always maintaining the same ratio.
a.
In this problem we can write a variation equation and solve for the constant of proportionality.
y = kx
The cost for each room is $27
27 = k(1)
k = 27
The constant of proportionality = 27
y = 27x
b.
The total cost is 256.50, the number of rooms can be calculated as;
256.50 = 27x
x = 256.50 / 27
x = 9.5
Approximating this, they can pay for 10 rooms.
Learn more on proportional relationship here;
https://brainly.com/question/12242745
#SPJ1
help fast please.........................
Answers
The type of angle in which angle 3 and angle 6 are, is that they are alternate interior angles ( option C)
What are angles on parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
Since line c and line b are parallel to each other and line a is the transversal that cut through both of them the angle on line a and line b will have the following characteristics;
They can be;
supplementary
alternate exterior
alternate interior
vertically opposite
and corresponding
The property between angle 3 and angle 6 is that they are alternate interior to each other.
Therefore angle 3 and angle 6 are alternate interior angles.
learn more about angle on parallel lines from
https://brainly.com/question/24607467
#SPJ1
Please answer this It would mean alot to me.
Answers
The expression 8x + 4y is not equivalent to 4(2x + 1). Therefore, 8x + 4y = 4(2x + y)
How to find equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Equivalent expressions are expressions that have similar value or worth but do not look the same.
Let's determine whether the expression 8x + 4y is equivalent to 4(2x + 1).
Let's factorise to know whether the expressions are equivalent.
Therefore, using the common factors,
8x + 4y = 4(2x + y)
Hence, the expression are not equivalent .
learn more on equivalent expression here: https://brainly.com/question/28170201
#SPJ1
Which points on the number line are included in the solution set of this inequality? (GIVING BRAINLIEST
Answers
Answer:
The points -3, 5 and 8 are included in the solution set
Step-by-step explanation:
2 ≤ |x-3| ≤ 6
x-3 ≥ 2 or x-3 ≤ -2 --> x ≥ 5 or x ≤ 1
-6 ≤ x-3 ≤ 6 --> -3 ≤ x ≤ 9
-9 and -5 are smaller than -3 so they don't hold for the second inequality. -3 fits in both. but 0 and 2 don't fit in the first one.
then 5 does and 8 is included too.
The points -3, 5 and 8 are included in the solution set
Sam average 13 points per game in her first three basketball games. She averaged 14.5 points in her first four games. How many points did he score in her fourth game?
Answers
Answer:
19
Step-by-step explanation:
13×3= 39
14.5×4= 58
58-39= 19
What is the area of the trapezoid with height 13 units
Answers
The area of the trapezoid is 2.2 square units
How to determine the valueThe formula for the area of a trapezoid is expressed as;
A = a+ b/h
Given that the parameters are;
A is the area of the trapezoida is the length of sideb is the length of its baseh is the heightSubstitute the values
Area = 15 + 7 + 7/13
Add the values
Area = 29/13
Divide the values
Area = 2.2 square units
Hence, the value is 2.2 square units
Learn about area at: https://brainly.com/question/25292087
#SPJ1
me ayudan a resolver esto?
Answers
Step-by-step explanation:
es 1
6/9+2/3+10/2(5)=
6+6+45/9=
57/9
es 2
-3/6-2/4-10/5(2)=
-6-6-24/12=
36/12=3
es 3
15/8-3/2+8/9=
135-108+64/72=
91/72
Question
Drag each description to the correct location on the table.
Examine the equation to determine if the descriptions listed are key features of the function or not.
Answers
Answer:
Key Feature: - decreasing, As x approaches -(infinite), y approaches (infinite), As x approaches (infinite), y approaches a constant.
Not a Key feature: increasing, As x approaches (infinite) y approaches (infinite), As x approaches -(infinite) y approaches -(infinite), & As x approaches -(infinite) y approaches a constant.
Step-by-step explanation:
Bananas are selling for $0.85 a pound. Milan spent $9.86 on bananas. How many pounds of bananas did Milan buy?
Answers
Answer:
11.6 lbs
Step-by-step explanation:
What is the equivalent property of 7(x+3)
Answers
Answer:
7x+21
Step-by-step explanation:
A plastic bin contains red, yellow, and green key chains. Out of 350 key chains, 10% are yellow. Of the remaining key chains, 3/5 are green. How many red key chains are inside the bin?
Answers
find the area of this shape. please help
Answers
Answer:
Step-by-step explanation:
Divide and Conquer:
Make shapes you know how to find the area of
(4x5.75)+8+4=35 cm^2
I don’t understand this
Answers
Answer:
9 to the 5th power
Step-by-
Answer:
n=5 I think...
Step-by-step explanation:
9^7/9^n = 9^2
Multiply by (n)
9^7-n = 9^2
7-n=2
7-n=2: n=5
-n=-5
Simplify:
n=5
fill in the mission numbers to make the fractions equivalent. 1/2 and /8= 4/12 and /60= 2/3 and /12= 4/4 and /8=
Answers
To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:
1/2 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
1/2 and 4/8
Now, the fractions are equivalent.
---
4/12 and __/60
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:
4/12 and 20/60
Now, the fractions are equivalent.
---
2/3 and __/12
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
2/3 and 8/12
Now, the fractions are equivalent.
---
4/4 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:
4/4 and 8/8
Now, the fractions are equivalent.
PLEASE HELP IMMEDIATELY!!!
Answers
A=gbb/2=15x24/2=180
2/8x+3/8(x-1)=4 solve for x
Answers
\(\dfrac 28 x + \dfrac 38 (x-1) = 4\\\\\implies \dfrac 18(2x + 3x -3) = 4\\\\\implies 5x -3 = 32\\\\\implies 5x = 32 +3 \\\\\implies 5x = 35\\\\\implies x = \dfrac{35}5\\\\\implies x = 7\)
Answer:
The value of x is 7.
Step-by-step explanation:
Question :
\({\implies{\sf{\dfrac{2}{8} x + \dfrac{3}{8}(x - 1) = 4}}}\)
Solution :
\({\implies{\sf{\dfrac{2}{8} x + \dfrac{3}{8}(x - 1) = 4}}}\)
\({\implies{\sf{\dfrac{2}{8} \times x + \dfrac{3}{8}(x - 1) = 4}}}\)
\({\implies{\sf{\dfrac{2 \times x}{8} + \dfrac{3(x - 1)}{8} = 4}}}\)
\({\implies{\sf{\dfrac{2x}{8} + \dfrac{3x - 3}{8} = 4}}}\)
\({\implies{\sf{\dfrac{2x + 3x - 3}{8} = 4}}}\)
\({\implies{\sf{\dfrac{5x - 3}{8} = 4}}}\)
\({\implies{\sf{{5x - 3} = 4 \times 8}}}\)
\({\implies{\sf{{5x - 3} =32}}}\)
\({\implies{\sf{5x = 32 + 3}}}\)
\({\implies{\sf{5x = 35}}}\)
\({\implies{\sf{x = 35 \div 5}}}\)
\({\implies{\sf{x = \dfrac{35}{5}}}}\)
\({\implies{\sf{x = \cancel{\dfrac{35}{5}}}}}\)
\({\implies{\sf{x = 7}}}\)
\(\star{\underline{\boxed{\sf{\pink{x = 7}}}}}\)
Hence, the value of x is 7.
\(\rule{300}{1.5}\)
Triviaaaa for you smart people, is Sixteen times some number equals 60, an equation or expression?
Answers
Answer:
an equation
Step-by-step explanation:
this is because there is an unknown value (some number)
the exact value of sin 5pi/12 is
Answers
The exact value of sin(5π/12) is (√6 + √2)/4
Calculating the exact value of sin 5pi/12From the question, we have the following parameters that can be used in our computation:
sin 5pi/12
Express properly
So, we have
sin(5π/12)
Convert the angle to degrees
This gives
sin(5π/12) = sin(5/12 * 180)
Evaluate
sin(5π/12) = sin(75)
The actual value of sin(75) is (√6 + √2)/4
This means that
sin(5π/12) = (√6 + √2)/4
Hence, the exact value of sin(5π/12) is (√6 + √2)/4
Read more about trigonometry function at
https://brainly.com/question/24349828
#SPJ1
The exact value of sin 5π/12 is (√6 + √2)/4
What is trigonometric function?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Angle in trigonometry can be measured in either degree or radian.
π is a measurement in radian which is equivalent to 180° in degrees.
Therefore:
5π/12 = 5 × 180/12
= 75°
Therefore sin5π/12 = sin75°
sin75 = sin( 45+30) = sin45cos30+ cos 45sin30
= 1/√2 × √3/2 + 1/√2 × 1/2
= √3/2√2 + 1/2√2
= (√3+1)/2√2
rationalizing;
(2√6 + 2√2)/8
dividing through by 2
=(√6 + √2)/4
therefore tan75 =(√6 + √2)/4
learn more about trigonometric functions from
https://brainly.com/question/25618616
#SPJ1
Use implicit differentiation to find dy/dx and d^2y/dx^2.
Answers
Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.
Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.
Given the equation x² + xy + y² = 5,
we can differentiate both sides with respect to x using the chain rule as follows:
2x + (x(dy/dx) + y) + 2y(dy/dx) = 0
Simplifying this equation yields:
(x + 2y)dy/dx = -(2x + y)
Hence, dy/dx = -(2x + y)/(x + 2y)
Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.
That is:
d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))
= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))
Simplifying this equation yields:
d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³
For more such questions on implicit differentiation visit:
https://brainly.com/question/25081524
#SPJ8
4
Calculate the area of the shaded region. Round to the nearest tenth, as needed.
59
1.3 m 1.7 m
Answers
Answer:
0.9m²
Step-by-step explanation:
Find the area of the larger circle, the radius is 0.85m because the diameter is double this - 1.7m:
a = πr² = π × (0.85)² = 289/400πFind the area of the smaller circle, the radius is 0.65 because the diameter is double this - 1.3m:
a = πr² = π × (0.65)² = 169/400πSubtract the two area:
289/400π - 169/400π = 120/400π = 3/10π or 0.942477.. ≈ 0.9m²
Marking as brainliest rn ! Write the congruent statement
Answers
Answer:
Same thing here as the last question, just matching congruent angles.
1. ΔXZY ≅ ΔQRP
2. ΔQRS ≅ ΔSCD
3. ΔGHI ≅ ΔGHT
Step-by-step explanation:
hope this helps. . .<3
good luck! UwU
Answer:
1.) ΔXZY ≅ ΔQRP
2.) ΔQRS ≅ ΔSCD
3.) ΔGHI ≅ ΔGHT
Hope this helps!
the perimeter of a triangle is 32 feet. One side of the triangle is 11 feet longer than the second side. The third side is 9 feet longer than the second side. Find the length of each side.
Answers
Answer:
One side - 15 feet
Second side - 4 feet
Third side - 13 feet
Step-by-step explanation:
Let's call the sides A B and C, respectively.
We know that:
A = B + 11
C = B + 9
and that
A + B + C = 32
Please note that we have 3 equations and 3 unknowns. We can solve this, we'll use substitution.
A + B + C = (B + 11) + B + (B + 9) = 32
3B + 20 = 32
3B = 12
B = 4
The sides have lengths of 4+11 = 15, 4 and 4+9 = 13. This is in fact a proper triangle (because the shorter sides add up to more than the longer side).