### Understanding Total Cost in ManufacturingThe **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.#### Example ProblemSuppose that a manufacturer of widgets has fixed costs of **$7000** per month and that the variable cost is **$16** per widget (so it costs **$16** to produce 1 widget).1. **Formulating the Total Cost Function** (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.) \[ C = \text{\$7000} + 16N \]2. **Calculating Specific Total Costs** (b) Express using functional notation the total cost if there are **200** widgets produced in a month. \[ C(200) = 7000 + 16 \cdot 200 \] Calculate the total cost if there are **200** widgets produced in a month. \[ C(200) = 7000 + 3200 = 10200 \] Thus, the total cost if there are 200 widgets produced in a month is **$10,200**.

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

Answered: The total cost C for a manufacturer…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

2. The local community hall is hired out at a rate of $20 per hour plus a fee of $60 for cleaning. (a) Write a formula relating total cost of hiring the hall to the number of hours required. Be sure to carefully define all variables that you use. (b) Complete the following table of values for the costs to hire the hall for the hours given Hours Required 1 2 3 4 Cost of Hall ($) (c) Plot the values from the table on a graph and draw a trend line. (d) Use your graph to determine the cost of hiring the hall for 4.5 hours. (e) If your group has only budgeted for a total of $130 for how long could they hire the hall?
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 $7000 per month and that the variable cost is $16 per widget (so it costs $16 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…
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.
The total number t of items that a manufacturing company can produce is directly proportional to the number n of employees.
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…
Gas mileage actually varies slightly with the driving speed of a car (as well as with highway vs. city driving). Suppose your car averages 29 miles per gallon on the highway if your average speed is 48 miles per hour, and it averages 26 miles per gallon on the highway if your average speed is 65 miles per hour. Answer parts (a) and (b) below. a. What is the driving time for a 2300-mile trip if you drive at an average speed of 48 miles per hour? What is the driving time at 65 miles per hour? The driving time at 48 miles per hour is hours. (Type an integer or decimal rounded to two decimal places as needed.) The driving time is at 65 miles per hour is (Round to two decimal places as needed.) b. Assume a gasoline price of $4.43 per gallon. What is the gasoline cost for a 2300-mile trip if you drive at an average speed of 48 miles per hour? What is the gasoline cost at 65 miles per hour? The gasoline cost at 48 miles per hour is $ (Round to two decimal places as needed.) hours. The…
Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $7900 per month. Materials and labor for each helmet of this model are $55, and the company sells this helmet to dealers for $85 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C(x) = (b) Write the function for total revenue R(x). R(x) = (c) Write the function for profit P(x). P(x) = (d) Find C(200). C(200) = Interpret C(200). O When this many helmets are produced the cost is $200. O This is the cost (in dollars) of producing 200 helmets. O For every additional helmet produced the cost increases by this much. O For each $1 increase in cost this many more helmets can be produced. Find R(200). R(200) =

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS