$MathMaster logo$

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)

Math question: What is the formula for finding the volume of a cube?

+

What is the value of sinh(-2.5) - cosh(1.4) + tanh(3.1) at x = 5?

+

What are the properties of complex conjugates?

+

New questions in Mathematics

How much volume of water in MegaLiters (ML) is required to irrigate 30 Hectare crop area with depth of 20mm?

Convert the following function from standard form to vertex form f(x) = x^2 + 7x - 1

Consider the relation R defined on the set of positive integers as (x,y) ∈ R if x divides y. Choose all the true statements. R is reflexive. R is symmetric. R is antisymmetric. R is transitive. R is a partial order. R is a total order. R is an equivalence relation.

Kayla has $8,836.00 in her savings account. The bank gives Kayla 5%of the amount of money in account as a customer bonus. What amount of money does the bank give Kayla? Justify your answer on a 6th grade level.

Given that y = ×(2x + 1)*, show that dy = (2x + 1)" (Ax + B) dx where n, A and B are constants to be found.

What’s 20% of 125?

Suppose 56% of politicians are lawyers if a random sample of size 873 is selected, what is the probability that the proportion of politicians who are lawyers will be less than 55% round your answer to four decimal places

In a normally distributed data set a mean of 31 where 95% of the data fall between 27.4 and 34.6, what would be the standard deviation of that data set?

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?

John he’s going to the carnival with his friends. He spends $25 on an admission ticket. He buys 10 games at X dollars each and two boxes of popcorn at Y dollars each. Write an expression to show the total cost of admission game, tickets and popcorn.

Use linear approximation to estimate the value of the sine of 31o.

During a month's time, an automobile sales person receives a 6% commission on the first $5000 in sales, a 7% commission on the next $5000 sales, 8% commission on anything over $10,000. What is her commission for $36,000 in sales?

The mass of 120 molecules of X2C4 is 9127.2 amu. Identify the unknown atom, X, by finding the atomic mass. The atomic mass of C is 12.01 amu/atom

solid obtained by rotation around the axis x = -1, the region delimited by x^2 - x + y = 0 and the abscissa axis

Find the set of points formed by the expression 𝜋<|𝑧−4+2𝑖|<3𝜋.

P 13. Let P a point inside of a square ABCD. Show that the perpendicular lines drawn from A, B, C, respectively D, to BP, CP, DP, respectively AP are concurrent. Use geometric rotation.

A candy manufacturer must monitor deviations in the amount of sugar in their products They want their products to meet standards. They selected a random sample of 20 candies and found that the sandard deviation of that sample is 1.7. What is the probabilty of finding a sample variance as high or higher if the population variance is actually 3277 Assume the population distribution is normal.

What is the set-off agreement? Make your own example, describe and put in T accounts how you record transactions.