$MathMaster logo$

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)

Find the volume V of a sphere with radius r using the formula V = (4/3)πr³.

+

How many ways can you arrange 6 different books on a shelf?

+

What is ⅔ of 150?

+

New questions in Mathematics

calculate the derivative by the limit definition: f(x) = 6x^3 + 2

Find an arc length parameterization of the curve that has the same orientation as the given curve and for which the reference point corresponds to t=0. Use an arc length s as a parameter. r(t) = 3(e^t) cos (t)i + 3(e^t)sin(t)j; 0<=t<=(3.14/2)

𝑦 = ( 𝑥2 − 3) (𝑥3 + 2 𝑥 + 1)

Investing equal amounts of money into each of five business ventures Let's say you plan. 20 to choose from If there are initiatives, how many different ones among 20 initiatives? five startups can be selected?

Suppose a large shipment of cell phones contain 21% defective. If the sample of size 204 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 4% round your answer to four decimal places

A regional candy factory sells a guava roll at a price of $48, the monthly fixed costs amount to $125,000 and the variable cost for making a guava roll is $28. Determine: a) The equation of the total income from the production of guava rolls.

How long will it take for $900 to become $5000 at an annual rate of 11.15% compounded bimonthly?

If f(x,y)=6xy^2+3y^3 find (∫3,-2) f(x,y)dx.

-3(-4x+5)=-6(7x-8)+9-10x

Calculate the value of a so that the vectors (2,2,−1),(3,4,2) and(a,2,3) are coplanar.

Exercise 1 An ejidal association wishes to determine the distribution for the three different crops that it can plant for the next season on its available 900 hectares. Information on the total available and how many resources are required for each hectare of cultivation is shown in the following tables: Total available resource Water 15,000 m3 Fertilizer 5,000 kg Labor 125 day laborers Requirements per cultivated hectare Corn Soybeans Wheat Water 15 25 20 Fertilizer 5 8 7 Labor** 1/8 1/5 1/4 *The data in fraction means that with one day laborer it will be possible to care for 8, 5 and 4 hectares respectively. * Sales of crops 1 and 3, according to information from the Department of Agriculture, are guaranteed and exceed the capacity of the cooperative. However, soybeans must be limited to a maximum of 150 hectares. On the other hand, the profits for each hectare of crop obtained are estimated at: $7,500 for corn, $8,500 for soybeans and $8,000 for wheat. The objectives are to determine: • How many hectares of each crop must be allocated so that the profit is maximum. R= • The estimated profits for the ejidal cooperative in the next growing season. R=

Use a pattern approach to explain why (-2)(-3)=6

If the regression equation is given by 4x –y + 5 = 0, then the slope of regression line of y on x is

X~N(2.6,1.44). find the P(X<3.1)

A hardware bill totals $857.63 with discounts of 5% and 3%. What is the net cost of the Material ?

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.

(6²-14)÷11•(-3)

2 - 6x = -16x + 28

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?