$MathMaster logo$

MathMaster

Home
general
marginal income when a hairdresser sets a fee of 4 per haircut she notices that the number of clients she serves in a week

Question

(Marginal income) When a hairdresser sets a fee of $4 per haircut, she notices that the number of clients she serves in a week is 100, on average. By raising the rate to $5, the number of customers per week drops to 80. Assuming a linear demand equation between the price and the number of customers, determine the marginal revenue function. Then find the price that produces zero marginal revenue.

257

likes

1287 views

Answer to a math question (Marginal income) When a hairdresser sets a fee of $4 per haircut, she notices that the number of clients she serves in a week is 100, on average. By raising the rate to $5, the number of customers per week drops to 80. Assuming a linear demand equation between the price and the number of customers, determine the marginal revenue function. Then find the price that produces zero marginal revenue.

$Expert avatar$

4.9

87 Answers

1. \text{Calculate the slope } m:

m = \frac{Q_2 - Q_1}{P_2 - P_1} = \frac{80 - 100}{5 - 4} = \frac{-20}{1} = -20

2. \text{Calculate the intercept } b \text{ using the point } (4, 100):

100 = -20 \cdot 4 + b

100 = -80 + b

b = 180

\text{Thus, the demand equation is:}

Q = -20P + 180

3. \text{Substitute the demand equation into the revenue function:}

R = P \cdot Q

R = P \cdot (-20P + 180)

R = -20P^2 + 180P

4. \text{Find the marginal revenue } MR \text{ by taking the derivative of } R:

MR = \frac{dR}{dP} = \frac{d}{dP} (-20P^2 + 180P)

MR = -40P + 180

5. \text{Set } MR = 0 \text{ and solve for } P:

-40P + 180 = 0

40P = 180

P = \frac{180}{40}

P = 4.5

\text{The price that produces zero marginal revenue is } \$4.50

Frequently asked questions (FAQs)

What is the value of f(x) = 3x^2 + 2x - 1 when x = 4?

+

What is the standard deviation of a dataset: 10, 12, 14, 16, 18?

+

Math Question: What is the limit as x approaches 0 of sin(x)/x?

+

New questions in Mathematics

reduction method 2x-y=13 x+y=-1

90 divided by 40

For a temperature range between 177 degrees Celsius to 213 degrees Celsius, what is the temperature range in degrees Fahrenheit.

Express the following numbers in decimal system, where the subscript indicates the base: 110101 (SUBINDEX=2)

A National Solidarity Bond offers A 5 year bond offering a gross return of 15% Calculate the AER for this investment. (Give your answer to two decimal places, no need for the percent or € sign in your answer)

According to a survey in a country 27% of adults do not own a credit card suppose a simple random sample of 800 adults is obtained . Describe the sampling distribution of P hat , the sample proportion of adults who do not own a credit card

There were no defectives in a sample of 1 light bulb does this sample provide sufficient evidence that in the warehouse with millions of light bulbs fewer than 10% are defective?

What is 28 marks out of 56 as a percentage

v Is the following statement a biconditional? If Shannon is watching a Tigers game, then it is on television.

Calculate the boiling temperature and freezing temperature at 1 atmosphere pressure of a solution formed by dissolving 123 grams of ferrous oxide in 1.890 grams of HCl.

19) If the temperature of -8°C decreases by 12°C, how much will it be? a)-20°C -4°C c) 4°C d) 20°C

The points (-5,-4) and (3,6) are the ends of the diameter of the circle calculate subequation

2.380× (1+0.05) / 0.95−0.05

A company has had the following data for two consecutive years. Total, asset item 3,100,500 euros 3,300,550 euros. Net amount of business figures 4,755,250 euros /5,100 euros Average number of workers employed during the year 64/70 You can present a balance sheet in an abbreviated form

A diamond ring was reduced from $999.99 to $689.99. Find the percent reduction in the price. Round the answer to the nearest tenth of a percent, if necessary.

Write an expression using compatible numbers that can be used to estimate the quotient 629\86

Given a circle 𝑘(𝑆; 𝑟 = 4 𝑐𝑚) and a line |𝐴𝐵| = 2 𝑐𝑚. Determine and construct the set of all centers of circles that touch circle 𝑘 and have radius 𝑟 = |𝐴𝐵|

What js the greatest 4-digit even number that can be formed by 3,6,1,4?

calculate the product of 4 and 1/8