1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
notka56 [123]
3 years ago
5

If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost func

tion C(x) given below. C(x) = 16,000 + 140x + 4x3/2 (a) Find the total cost at a production level of 1000 units. (Round your answer to the nearest cent.)(b) Find the average cost at a production level of 1000 units. (Round your answer to the nearest cent.) (c) Find the marginal cost at a production level of 1000 units. (Round your answer to the nearest cent.)(d) Find the production level that will minimize the average cost. (Round your answer to the nearest whole number.) (e) What is the minimum average cost? (Round your answer to the nearest dollar.)
Business
1 answer:
ANTONII [103]3 years ago
6 0

Answer:

Following are the solution to the question:

Explanation:

Calculating the total cost:

C(x) = 2,000 + 140x + \frac{4x^3}{2}

Calculating the marginal cost:

M(x) = C'(x) = 140 + 6 \times \frac{1}{2}

Calculating the average cost:

A( x ) =\frac{ C( x )}{x} = 2,000x-1 + 140 + 4\times \frac{1}{2}

Calculating the marginal average cost:

m( x ) = A'( x ) = -2,000x-2 + 2x-\frac{1}{2}

In point  (a)

C( 1,000 )

              = 2,000 + 140( 1,000 ) + 4( 1,000)^{\frac{3}{2}}\\\\=  \$ \ 268,491.106  \\\\ = \$ \ 268,491.11

In point(b)

A( 1,000 )

               = 2,000( 1,000 )-1 + 140 + 4( 1,000 )^{\frac{1 }{2}}\\\\= \frac{\$ \ 268.491106} {unit}\\\\= \frac{\$ \ 268.49}{ unit}

In point (c)

M( 1,000)

              = 140 + 6( 1,000 )^{\frac{1}{2}}\\\\= \frac{\$ \ 329.73666}{unit}\\\\= \frac{ \$ \  329.74}{ unit}

In point (d)  

Calculating the average cost:

A'( x ) = m( x ) = -2,000x-2 + 2x- \frac{1}{2}\\\\A'( x ) = 0 = -2,000x-2 + 2x-\frac{1}{2}= 0\\\\multiply \ by \ 2\\\\\to -2,000 + 2 \times \frac{x^3}{2}= 0 \\\\\to 2\times \frac{x^3}{2} = 2,000 \\\\\to \frac{x^3}{2} = \frac{2,000}{2} \\\\ \to \frac{x^3}{2}= 1,000 \\\\\to x = ( 1,000 )^{\frac{2}{3}}\\\\ \to  100 \ units

In point (e)

A( 100 )

            = 2,000( 100 )-1 + 140 + 4( 100 )^{\frac{1}{2}}\\\\= \frac{ \$ \ 200}{unit}

You might be interested in
Assume the world market for oil is competitive and that the marginal cost of producing another barrel of oil is $79.40 and the m
Alona [7]

Answer:

b. Increase by $2.20

Explanation:

Economic Surplus is the total benefit to society from production.

If an additional unit is produced the additional cost will be $79.40 and it will the additional benefit of $81.60.

So the surplus = benefit - cost = $81.60 - $79.40 = $.2.20

They are marginal quantities (change made by additional unit) so everything has been taken into account for the deriving of change to surplus.

3 0
3 years ago
Sheffield Corp. produces three versions of baseball bats: wood, aluminum, and hard rubber. A condensed segmented income statemen
nekit [7.7K]

Answer:

The correct answer is D.

Explanation:

Giving the following information:

Sales=$775000

Variable expenses= 523000

Contribution margin= 252000

Fixed expenses= 132000

Net income= $120000

Hard Rubber:

Sales=$65000

Variable expenses=58000

Contribution margin= 7000

Fixed expenses= 22000

Net income= -15000

New net income= 120,000 + 15,000 - 22,000= 113,000

6 0
3 years ago
The student-run newspaper asks students to visit a web page and respond to questions regarding a proposed tuition increase. Only
disa [49]

Answer:

C) both anonymous and confidential

Explanation:

  • As the student-run, the new paper and ask other students to visit a link firm the new paper and respond to those questions and the responses for only those questions were recorded.  
  • This indicates that the newspaper survey is anonymous and confidential as the ant student can fill the survey and the information that is confidential as none outside the newspaper has access to those responses.
6 0
3 years ago
Hielta Oy, a Finnish company, processes wood pulp for various manufacturers of paper products. Data relating to tons of pulp pro
bonufazy [111]

Answer:

the equivalent units of production for materials = 352,616 units,

the equivalent units of production for for labor and overhead (conversion) = 339,304 units

Explanation:

First Determine the physical units that were Completed and Transferred out

<em>Units Completed and Transferred = Units in Opening Work In Process  + Units Started During the Year - Units in Closing Work In Process</em>

                                                        = 80,400 + 301,400 - 51,200

                                                        = 330,600

Calculation of Equivalent Units of Production for

1. Materials

Units Completed and Transferred ( 330,600 × 100%)   = 330,600

Units in Closing Work In Process ( 51,200 × 43%)          =   22,016

Total Equivalent Units of Production for Materials         = 352,616

2. Labor and Overhead

Units Completed and Transferred ( 330,600 × 100%)   = 330,600

Units in Closing Work In Process ( 51,200 × 17%)          =      8,704

Total Equivalent Units of Production for Conversion    = 339,304

3 0
3 years ago
Rector Corporation is examining its quality control program. Which of the following statements​ is/are correct? I. Rework costs
Andre45 [30]

Answer:

II. Prevention costs are costs that are incurred to prevent the sale and production of defective units.

8 0
3 years ago
Other questions:
  • What is the National Labor Relations Board responsible for?
    9·1 answer
  • REM Real Estate received a check for $27,000 on July 1 which represents a 6 month advance payment of rent on a building it rents
    14·1 answer
  • Which countries were involved in the central powers alliance.
    13·1 answer
  • The price elasticity of demand for gasoline in the short run has been estimated to be 0.4. If a war in the Middle East causes th
    11·1 answer
  • Michael wanted to build a small princess castle for his daughter in the backyard. He decided to turn it into a do-it-yourself pr
    7·1 answer
  • An investor contributes $100,000 of cash to a partnership and signs a $200,000 recourse note. During the first year, the investo
    5·1 answer
  • The discounted payback period for a project will be _______ the payback period for the project given a positive, non-zero discou
    9·1 answer
  • Do lenders always accept applications for credit?
    7·1 answer
  • I WILL GIVE BRAINLIEST
    13·1 answer
  • Financial statements can be prepared _____. (select all that apply.) multiple select question.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!