Results 1 to 3 of 3

Math Help - Break Even + equilibrium questions

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    41

    Break Even + equilibrium questions

    3 somewhat similar questions:

    A manufacturer has monthly fixed costs of 112000 dollars and a production cost of 11 dollars for each unit produced. The product sells for 21 dollars per unit.
    i) The cost function is C(x) = ___________
    ii) The revenue function is R (x) = _________
    iii) The profit function is P(x) = ___________
    iv) Compute the profit (loss) corresponding to a production level of 5780 units: ______ dollars
    v) Compute the profit (loss) corresponding to a production level of 14800 units: ________ dollars

    Break - even

    A company produces a consumer level scanner at a price of 57 dollars per unit and sells it for 64 dollars per unit. The monthly fxed costs inccured by the company are 27097 dollars.
    Compute the break even quantity: _________ units
    Compute the break-even revenue: ________ dollers per month.
    What should be the level in sales in order for the company to realize a 5% profit over the cost of producing the scanners? ______ units. (round your anwser to the nearest integer)

    Market equilibrium

    The quantity demanded per month of a certain CD burner is 880 when the price is 138 dollars. The quantity demanded per month is 715 when the price is 153 dollars. The suppliers will not market any CD burners when the price is 50 dollars or less. At a unit price of 53 dollars they are willing to make available only 30 units in the market. Under the assumptions that both supply and demand are linear.
    i) Find the demand equation: y= ___________
    ii) Find the supply equation: y= ___________
    iii) Find the Equilibrium price: ______________ dollars
    iv) Find the equilibrium quantity: _____________ units
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member DeMath's Avatar
    Joined
    Nov 2008
    From
    Moscow
    Posts
    473
    Thanks
    5
    Quote Originally Posted by B-lap View Post
    3 somewhat similar questions:

    A manufacturer has monthly fixed costs of 112000 dollars and a production cost of 11 dollars for each unit produced. The product sells for 21 dollars per unit.
    i) The cost function is C(x) = ___________
    ii) The revenue function is R (x) = _________
    iii) The profit function is P(x) = ___________
    iv) Compute the profit (loss) corresponding to a production level of 5780 units: ______ dollars
    v) Compute the profit (loss) corresponding to a production level of 14800 units: ________ dollars
    i) You have
    - total fixed costs function FC(x)=112'000;
    - total variable costs function VC(x)=11x.

    Consequently, you get C(x) =FC(x)+VC(x)=112'000+11x.

    ii) The revenue function is R(x)=21x.

    iii) The profit function is P(x)=R(x)-C(x)=21-(112'000+11x)=10x-112'000.

    iv) Compute the profit (loss) corresponding to a production level of 5'780 units:

    \quad P(5'780)=10 \cdot 5'780 - 112'000 = 57'780-112'000 =-54'220 dollars (ie loss).

    v) Compute the profit (loss) corresponding to a production level of 14'800 units:

    \quad P(14'800)=10 \cdot 14'800 - 112'000 = 148'000-112'000 =36'000 dollars (ie profit).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member DeMath's Avatar
    Joined
    Nov 2008
    From
    Moscow
    Posts
    473
    Thanks
    5
    Quote Originally Posted by B-lap View Post
    3 somewhat similar questions:

    Break - even

    A company produces a consumer level scanner at a price of 57 dollars per unit and sells it for 64 dollars per unit. The monthly fxed costs inccured by the company are 27097 dollars.
    Compute the break even quantity: _________ units
    Compute the break-even revenue: ________ dollers per month.
    What should be the level in sales in order for the company to realize a 5% profit over the cost of producing the scanners? ______ units. (round your anwser to the nearest integer)

    1. BEQ=\frac{TFC}{P-VC}, where

    - TFC is a total fixed costs;
    - VC is a variable costs per unit;
    - P is a sell price per unit.

    Compute the break even quantity: BEQ=\frac{27'097}{64-57}= \frac{27'097}{7}=3'871 units (per month).


    2. Compute the break-even revenue: BEQ \cdot P=3'871 \cdot 64=247'744 dollars (per month).


    3. What should be the level in sales in order for the company to realize a 5% profit over the cost of producing the scanners? 6'856 units. (round your anwser to the nearest integer)

    Solution:
    Let x - the level in sales (units) in order for the company to realize a 5\% profit over the cost of producing the scanners, then, by the condition of your task, you let

    P \cdot x - (TFC + VC \cdot x) = 0.05 \cdot (TFC + VC \cdot x)

    P \cdot x - 1.05 \cdot VC \cdot x = 1.05 \cdot TFC;

    x = \frac{1.05 \cdot TFC}{P - 1.05 \cdot VC} =\frac{TFC}{\frac{P}{1.05}-VC}=\frac{27'097}{\frac{64}{1.05}-57}=\frac{569'037}{83} \approx 6'856 units.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Break even
    Posted in the Business Math Forum
    Replies: 2
    Last Post: February 12th 2010, 03:52 AM
  2. Break Even Point
    Posted in the Business Math Forum
    Replies: 2
    Last Post: October 19th 2009, 11:41 AM
  3. how to break it into dx and dy
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 13th 2009, 11:56 PM
  4. Can someone please break this down for me?
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 6th 2008, 08:51 PM
  5. break even help
    Posted in the Business Math Forum
    Replies: 0
    Last Post: February 21st 2007, 07:51 AM

Search Tags


/mathhelpforum @mathhelpforum