$MathMaster logo$

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 relationship between the medians and centroid of a triangle?

+

What is the simplified form of √(15) - 2√(6) + 3√(5)?

+

Question: What is the formula for finding the surface area of a cube, and what is the formula for calculating its volume?

+

New questions in Mathematics

a ferry travels 1/6 of the distance between two ports in 3/7 hour. the ferry travels at a constant rate. at this rate, what fraction of the distance between the two ports can the ferry travel in one hour?

QUESTION l. An investigation has been carried out in a region to know the perception of "citizen insecurity" of its inhabitants. 1,270 people in the region were interviewed, of which 27.1% responded that it was a "serious" problem. Knowing that this opinion was previously held by 25.3% of the population of that region, we want to know if said opinion has changed significantly for a confidence level of 97.2%. Taking this statement into account, the following is requested: a) Critical value of the contrast statistic. b) Solve the hypothesis test and indicate what conclusion we can reach. c) P-value of contrast.

What is the amount of interest of 75,000 at 3.45% per year, at the end of 12 years and 6 months?

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.

Let I ⊂ R be a bounded and nonempty interval. Show that there are numbers a, b ∈ R with a ≤ b and I =[a,b] or I =[a,b) or I =(a,b] or I =(a,b)

Let f(x) = x² − 1. Find the equation of the tangent line to the graph of f at the point x0 = 2.

How many anagrams of the word SROMEC there that do not contain STROM, MOST, MOC or CEST as a subword? By subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.

find x in the equation 2x-4=6

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.

Scores are normally distributed with a mean of 25 and standard deviation of 5. Find the probability that sixteen randomly selected students have a mean score that is less than 24.

A bag has 4 green lollipops, 3 white lollipops, and 1 black lollipop. What is the probability of drawing a white lollipop?

Derivative of 2x

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

y′ = 2x + 3y x′ = 7x − 4y x(0) = 2 y(0) = −1 sisteminin ¸c¨oz¨um¨un¨u bulunuz. (Lineer Denk. Sis.)

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

draw the condensed formula fpr 3,3,4 triethylnonane

The supply of a good registers periodic increases. With each increase in the offer, the total receipts of the bidders increase. Indicate the correct statement: a) demand is elastic b) demand is inelastic c) supply is inelastic d) supply has unit elasticity.

Write an equation of the affine function whose graph is perpendicular to the graph of f(x) = 5x − 1 and passes through the point (5, 20).

An invoice for €2,880 plus default interest of €48.40 was paid on October 28th. Interest rate 5.5%. When was the bill due?

Construct a set of six pieces of data with mean, median, and midrange of 67 and where no two pieces of data are the same.