2. A company has determined that the demand function for a certain couch is given by p = 4000 - 0.25x, where p is the price per couch and x is the number of couches sold. The fixed costs associated with producing a line of couches is $500,000, and each couch costs $280 to make. a. Start by finding functions to represent the revenue b. and the total cost c. then find a function for profit d. Determine how many couches should be manufactured and sold in order to maximize profit. Show Work and Write a Sentence!

2. A company has determined that the demand function for a certain couch is given by p = 4000 - 0.25x, where p is the price per couch and x is the number of couches sold. The fixed costs associated with producing a line of couches is $500,000, and each couch costs $280 to make. a. Start by finding functions to represent the revenue b. and the total cost c. then find a function for profit d. Determine how many couches should be manufactured and sold in order to maximize profit. Show Work and Write a Sentence!

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Suppose that a computer software company produces and sells a new operating system at a cost of $55…

A: The cost of new operating system is $55 per copy The fixed cost is $15,000 per month. If the number…

Q: The total cost C for a manufacturer during a given time period is a function of the number N of…

Q: (a) Verify that the formula p = 50 - 0.04N, where p is the price in dollars, gives the same values…

A: Given the price function p=50-0.04N.

Q: Suppose the supply for a certain textbook is given by p = 9ʻ and demand is given by p= - (a) How…

A: Here the supply for a certain textbook is given by p=15q2...............(1) and demand is given by…

Q: As the selling price of a product increases, demand decreases. Fewer people will buy a product if it…

Q: The total cost C for a manufacturer during a given time period is a function of the number N of…

A: Given that the total cost can be calculated as the sum of fixed cost and the product of the variable…

Q: A store can sell 400 candy bars per week when the price is $0.50 per candy bar and they can sell 350…

Q: he total cost C for a manufacturer during a given time period is a function of the number N of items…

A: Given that: suppose that a manufacturer of vidgets has fixed costs of $5000 per month and that the…

Q: Suppose that a manufacturer of widgets has fixed costs of $9000 per month and that the variable cost…

Q: The manufacturer has developed the following table showing the highest price p, in dollars, of a…

A: Given : The formula p = 50 − 0.04 N, where p is the price in dollars . To determine : (a) Use the…

Q: 6. Jocelyn's Cookie Company makes and sells cookies. Each cookie costs $1.58 to make, and the fixed…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: You sell candy at an event to make money. When candy are sold for $1.10 per bag, approximately 625…

Q: The total cost C for a manufacturer during a given time period is a function of the number N of…

A: Given : a manufacturer of widgets has fixed costs of $7000 per month and that the variable cost is…

Q: A company is planning to manufacture mountain bikes. Fixed monthly cost will be $300,000 and it will…

A: Number of mountain bikes are x The variable cost of producing each mountain bike is $ 200. So,…

Q: A contractor purchases a backhoe for $37, 300 Fuel and standard maintenance cost $5.95 per hour, and…

A: Given query is to find cost, revenue and profit function.

Question

2. A company has determined that the demand function for a certain couch is given by p = 4000 - 0.25x,
where p is the price per couch and x is the number of couches sold. The fixed costs associated with
producing a line of couches is $500,000, and each couch costs $280 to make.
a. Start by finding functions to represent the revenue
b. and the total cost
c. then find a function for profit
d. Determine how many couches should be manufactured and sold in order to maximize profit.
Show Work and Write a Sentence!

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: Calculation of to determine the revenue function and total cost for the given problem

VIEW

Step 3: Calculation of to determine profit function and number of manufactured couches for maximum profit

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

For part d, you cannot use calculus!

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

A company produces very unusual CD's for which the variable cost is $ 11 per CD and the fixed costs are $ 35000. They will sell the CD's for $ 55 each. Let a be the number of CD's produced. Write the total cost C as a function of the number of CD's produced. C = $ Write the total revenue R as a function of the number of CD's produced. R= $ Write the total profit P as a function of the number of CD's produced. P = $ Find the number of CD's which must be produced to break even. The number of CD's which must be produced to break even is
The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs.Suppose that a manufacturer of widgets has fixed costs of $9000 per month and that the variable cost is $14 per widget (so it costs $14 to produce 1 widget). (a) Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. (Use N as the number of widgets produced in a month.)C = (b) Express using functional notation the total cost if there are 225 widgets produced in a month.C( )Calculate the total cost if there are 225…
Suppose that Alexander’s Coffee Shop has fixed costs of $18 and variable costs per unit of $4. The demand function for the coffee shop is P = 24 − 2Q. Given the demand and cost functions, calculate the maximum profit that Alexander’s Coffee Shop can earn.
When Green Eggs and Ham are sold for $4.00 per apple at Whoville, approximately 2500 servings are sold. When the price is raised to $4.50 per Green Eggs and Ham, the number of servings sold drops to 2250. The cost of producing and shipping the Green Eggs and Ham can be modeled by, C = 3000 + .6x Assuming that the demand function is linear, what price will yield a maximum profit
If x represents the number of items produced, (a) write a cost function, (b) find a revenue function if each item sells for the price given, (c) state the profit function, (d) determine analytically how many items must be produced before a profit is realized (assume whole numbers of items), and (e) support the results of part (d) graphically. The fixed cost is $600, the cost to produce an item is $25, and the selling price of the item is $50. (a) The cost function is C(x) = (Simplify your answer. Do not factor.) (b) The revenue function is R(x)= (Simplify your answer. Do not factor.) (c) The profit function is P(x) = (Simplify your answer. Do not factor.) ← (d) At least items must be produced before a profit is shown. (Type a whole number.) (e) Choose the correct graph to the right. O A. 2100 O C. Dollars Items produced 2100 Items produced Q O B. 2100 O D. Dollars 2100 Items produced Items produced Q ✔
A firm sells a product for $80 per unit. Raw material costs are$12,50 per unit, labor costs are $27,50 per unit, and annual fixedcosts are $260,000.a. Determine the profit function P(x), where x equals the numberof units sold.b. How many units would have to be sold to earn an annualprofit of $250,000.
The marketing department of a company estimates that the demand for a product is given by p = 100 - 0.0001x, where p is the price per unit and x is the number of units. The cost C of producing x units is given by C = 310,000 + 25x and the profit P for producing and selling x units is given by P = R - C = xp – C. Sketch the graph of the profit function. P FA 15 000 000 15 000 000 10 000 000 10 000 000 5 000 000 5000 000 1 2 3 4 5 7 8 9 1 2 3 4 5 6 8 9 1 = 100,000 1= 100,000 MacBook DII 888 F9 F8 F7 F4 F5 F3 F1 * & $ % @ # 8 9 2 3 4 T Y Q W K G H .. . - < (O
Given that a firm has a demand equation q = 3p - 40, for 0 < p < 100, where p represents price in dollars and q is quantity of units demanded. Write out the Revenue function. What is the range of revenue this firm expects to generate from the sale of its product?