Calculus-Math

The ordering and transportation cost C for components used in a manufacturing process is approximated by the function below, where C is measured in thousands of dollars and x is the order size in hundreds.
C(x) = 12((1/x)+((x)/(x+3)))

(a) Verify that C(2) = C(15).
C(2) = 54/5


C(15) = 54/5



(b) According to Rolle's Theorem, the rate of change of the cost must by 0 for some order size in the interval (2, 15). Find that order size. (Round your answer to the nearest whole number.)

What is the answer to part b? I found the the derivative of C(x) and set it equal to zero and got approximately 4, but that isn't the right answer. Please help!!!

  1. 👍 0
  2. 👎 0
  3. 👁 1,611
  1. Rolle's Theorem says that since C(2)=C(15), there is some value 2<c<15 such that C'(c) = 0.

    dC/dx = 12(2x^2-6x-9)/(x(x+3))^2
    dC/dx=0 when 2x^2-6x-9=0, or
    x = 3/2 (1±√3)
    or, x = -1.1, 4.1

    So, your answer of 4 is correct. The graph at

    http://www.wolframalpha.com/input/?i=12%28%281%2Fx%29%2B%28%28x%29%2F%28x%2B3%29%29%29+

    shows the minimum in the desired interval, where C' is zero.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Business

    Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas’s fastest moving inventory item has a demand of 6000 units per year. The cost of each

  2. Accounting

    Department J had no work in process at the beginning of the period, 18,000 units were completed during the period, 2,000 units were 30% completed at the end of the period, and the following manufacturing costs were debited to the

  3. Social Studies

    Which economic activity was the first to be affected by the Industrial Revolution? A. textile manufacturing B. coal mining C. agriculture D. transportation I Think It's D....

  4. Accounting 7

    Job 31 has a direct materials cost of $300 and a total manufacturing cost of $900. Overhead is applied to jobs at a rate of 200 percent of direct labor cost. Use the relationships among total manufacturing costs, conversion cost,

  1. statistics, please help

    Thaarugo, inc., produces a GPS device that is becoming popular in parts of scandinavia, When thaarugo produces one of these, a printed circuit board (PCB) is used, and it is populated with several electronic components, Thaarugo

  2. accounting

    P20-2A For the year ended December 31, 2010, the job cost sheets of DeVoe Company contained the following data. Job Number Explanation Direct Materials Direct Labor Manufacturing Overhead Total Costs 7640 Balance 1/1 $25,000

  3. Accounting

    Department S had no work in process at the beginning of the period , 18,000 units were started during the period, 2,000 units were 30% completed at the end of the period, and the following manufacturing costs were debited to the

  4. science

    Designing and building new types of automobiles can cost manufacturing companies large amounts of resources. How do many engineers and companies solve this problem when introducing a new design? A) Find the cheapest materials and

  1. math

    The cost of manufacturing a semi-circular window is the cost of the glass pane together with the cost of the framing material. When ordering this window, a customer specifies the length of the base of the window, shown as l l . If

  2. Social Studies! 4 questions!

    1. Which sector of the Midwest economy is the biggest? A. agriculture B. industry C. services D. transportation ***** 2. Where was the world's first skyscraper located? A. Detroit B. St. Louis C. Minneapolis***** D. Chicago 3.

  3. math

    Last year Essex Manufacturing paid $3500 for utilities. This year the company used energy-saving techniques to reduce the utility bills by 13% of last year's cost. What was the cost of utilities for Essex Manufacturing this year?

  4. math

    A piano manufacturer has a daily fixed cost of $1200 and a marginal cost of $1500 per piano. Find the cost C(x) of manufacturing x pianos in onde day. Use your function to answer the following questions: a)On a given day, what is

You can view more similar questions or ask a new question.