The total revenue function for a product is given byR = 330x dollars, and the total cost function for this sameproduct is given by C = 3000 + 20x + x², where C ismeasured in dollars. For both functions, the input x is thenumber of units produced and sold.a. Form the profit function for this product from the twogiven functions.b. What is the profit when 8 units are produced and sold?c. What is the profit when 18 units are producedand sold?d. How many units must be sold to break even onthis product?a. Write the profit function.P(x) =(Simplify your answer.)b. When 8 units are produced and sold, there is aof $.(Simplify your answer.)c. When 18 units are produced and sold, there isaof $.(Simplify your answer.)d. The number of units that must be sold to breakeven on this product is.(Simplify your answer. Use a comma to separateanswers as needed.)

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Answered: The total revenue function for a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A company is planning to manufacture mountain bikes. Fixed monthly cost will be $300,000 and it will cost $200 to produce each bicycle. A. Write the cost function, C, of producing x mountain bikes. C(x) = per month B. Write the average cost function, C, of producing x mountain bikes. C(x) = per month %3D C. How many mountain bikes must be produced each month for the company to have an average cost of $300 per bike? must be produced each month. Enter your answer in each of the answer boxes.
A contractor purchases a backhoe for $37, 300. Fuel and standard maintenance cost $5.95 per hour, and the operator is paid $12.03 per hour. a. Write a cost function for the cost C(z) of operating the backhoe for hours. Be sure to include the purchase price in the cost function. Cost function: C(z) = dollars b. If customers pay $27.77 per hour for the contractor's backhoe service, write the revenue function R(z) for the amount of revenue gained from a hours of use. Revenue function: R(x) = I c. Write the profit function P(x) for the amount of profit gained from a hours of use. Profit function: P(x) = dollars dollars d. How many hours must the backhoe be used in order to break even (assume that part of an hour counts as a whole hour)? In order for the contractor to break even, customers need to pay to use the backhoe for a total of hours.
It costs a publishing company $60,001 in fixed costs and it costs $4.20 per book to produce them. The publisher sells the books for $10 each. What are the revenue and cost functions? Find and interpret the break-even point.
The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $8000.a. Find the cost function CC when xx energy drinks are manufactured.C(x)=b. Find the revenue function RR when xx drinks are sold.R(x)=c. Find the break-even point by any method.x= drinks
A candy producer charges $4 for its special lollipop. It costs them $1.50 to produce each lollipop. Additionally, they spend $370 per week to maintain the production. A. Let C represent the weekly cost in dollars and let x represent the number of lollipops produced. Write down the producer’s weekly cost function. B. Let R represent the revenue in dollars and let x represent the number of lollipops sold. Write down the producer’s revenue function.
If the price (in dollars) of a product is given by P(x) 1024 + 1500, where x represents the demand for the product, find the rate of change of price when the demand is 32 units.

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