Business, 18.02.2020 02:18 angiebailey1605

The revenue (in dollars) from the sale of x car seats for infants is given by the following function.

R (x)= 64x - 0.020 x^2 0 <= x <= 3200

a. Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats.
b. Use the four-step process to find R (x).
c. Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results.

Answers: 1

Show answers

Answers

Answer from: vannitling12p4w44f

a) Average rate of change: 23 $/seat

b) R'(x)=64-0.040x

c) R(1000) = 44,000 $, R'(1000) = 23 $seat

Explanation:

The average rate of change of a function f(x) in a certain interval $x_1\leq x\leq x_2$ is given by

$r=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

The function that gives the revenue in dollars from the sale of x car seats is

R(x)=64x-0.020x^2

where

0 <= x <= 3200

We want to calculate the average rate of change in the interval

$x_1 = 1000\\x_2 = 1050$

Calculating the value of the revenue function for these two values,

$f(x_1)=64\cdot 1000 - 0.020\cdot 1000^2=44,000\\f(x_2)=64\cdot 1050 -0.020 \cdot 1050^2=45,150$

Therefore, the average rate of change is

$r=\frac{45,150-44,000}{1050-1000}=23$

Here we want to find R'(x), the derivative of R(x).

Step 1:

Evaluating R(x+h) :

R(x+h)=64(x+h)-0.020(x+h)^2=64x+64h-0.020x^2-0.040hx-0.020h^2

Step 2:

Evaluating R(x+h)-R(x) :

$R(x+h)-R(x)=64x+64h-0.020x^2-0.040hx-0.020h^2-(64x-0.020x^2)=\\=64h-0.040hx-0.020h^2$

Step 3:

Evaluating $\frac{R(x+h)-R(x)}{h}=\frac{64h-0.040hx-0.020h^2}{h}=64-0.040x-0.020h$

Step 4:

Find the limit for $h\rightarrow 0$ :

$\lim_{h \to 0} (64-0.040x-0.020h) =64-0.040x$

When the production level is 1000 car seats,

x = 1000

Therefore the revenue is:

$R(1000)=64\cdot 1000-0.020\cdot 1000^2=44,000$

The instantaneous rate of change of revenue instead is given by the derivative of R(x), found in part b):

R'(x)=64-0.040 x

Therefore, substituting x = 1000,

$R'(1000)=64-0.040\cdot 1000=24$

The two data can be interpreted as follows:

- When the production level is 1000 car seats, the revenue is 44,000$

- When the production level is 1000 car seats, the revenue is changing by 23$/new seat produced

Answer from: Quest

They are enjoying the advantage of independence while running their own small business. they can go where they want when they want to, because they control the restaurant's hours. they can also make time for life emergencies, and set the hours to be when they do the best cooking.

Answer from: Quest

$527.7.if the following was the question $527.7 is the answer.students who are trying to raise funds have an agreement with a local pizza chain. the chain has agreed to sell them pizzas at a discount, which the students can then resell to families in the local community for a profit. it is expected that of the 500 families in the community, at most 70% will buy pizza. based on a survey of their personal preferences, the students believe that they should order no more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. they also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. they make a profit of $1.45, $1.75, and $1.98, respectively, for each cheese, pepperoni, and vegetarian pizza they resell. how many pizzas of each type should they buy?

Another question on Business

Business, 22.06.2019 02:00

Southeastern bell stocks a certain switch connector at its central warehouse for supplying field service offices. the yearly demand for these connectors is 15,000 units. southeastern estimates its annual holding cost for this item to be $25 per unit. the cost to place and process an order from the supplier is $75. the company operates 300 days per year, and the lead time to receive an order from the supplier is 2 working days.a) find the economic order quantity.b) find the annual holding costs.c) find the annual ordering costs.d) what is the reorder point?

Answers: 2

Answer

Business, 22.06.2019 20:30

Juanita and sam attend a beach party and notice that the local beach appears to have a great deal more trash washed up on shore than it did when they were young. the water doesn't appear nearly as clear, and there seems to be less evidence of small water creatures living in the shallows. an afternoon at the local library convinces them that one major cause is the new factory nearby. after some discussion, they decide their next step should be identifying the cause of the changes identifying the problem picketing the guilty factory lobbying their elected representatives to complain about the problem talking to a local environmental group about solutions

Answers: 3

Answer

Business, 22.06.2019 22:30

Ellen and george work for the same company. ellen, a gen xer, really appreciates the flextime opportunities, while george, a baby boomer, takes advantage of the free computer training offered at the company. these policies are examples of

Answers: 3

Answer

Business, 23.06.2019 01:00

Sarah is an accountant with desires to open her own business. she is looking for office space at a reasonable rate along with internet service. of the conditions that need to be put in place for the entrepreneurial ecosystem, she needs

Answers: 1

Answer

You know the right answer?

The revenue (in dollars) from the sale of x car seats for infants is given by the following function...

Questions