Results 1 to 9 of 9

Math Help - Break even point

  1. #1
    Junior Member
    Joined
    Jun 2010
    Posts
    52

    Break even point

    So here's the question that i have and i hope someone can help me with this because i am kind of stumped. MY main struggle is determining which is VC and which is FC.

    John and Jack have opened a shop in Kelowna to build customized patio furniture. The projected selling price of a patio set will be $3,000. They estimate that the table will use twenty (20) board feet of lumber at a cost of $12 per board foot, $10 per table for hardware, and another $15 for custom finishing materials such as stain, varnish, or painting. Each patio set comes with four (4) chairs. Each chair will use six (6) board feet of lumber, $6 for hardware, and $10 for finishing materials. They estimate the labour time per table to be twenty-five (25) hours, and per chair, ten (10) hours for construction and finishing work. John found warehouse space that they can rent for $2,300 per month including heat. Other utilities will be $275 per month. Other required costs are insurance at $3,500 per year. They will pay themselves $20 per hour (treat this as a variable cost). They will pay a sales commission (based on selling price) of 4% per complete set sold. Jack estimates that they can build 125 sets per year.



    i am asked to find....


    1. How many patio sets must they construct to break-even? Calculate the break-even point in:
    a. units.
    b. sales dollars.






    Thanks in advance..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by petedam View Post
    So here's the question that i have and i hope someone can help me with this because i am kind of stumped. MY main struggle is determining which is VC and which is FC.

    John and Jack have opened a shop in Kelowna to build customized patio furniture. The projected selling price of a patio set will be $3,000. They estimate that the table will use twenty (20) board feet of lumber at a cost of $12 per board foot, $10 per table for hardware, and another $15 for custom finishing materials such as stain, varnish, or painting. Each patio set comes with four (4) chairs. Each chair will use six (6) board feet of lumber, $6 for hardware, and $10 for finishing materials. They estimate the labour time per table to be twenty-five (25) hours, and per chair, ten (10) hours for construction and finishing work. John found warehouse space that they can rent for $2,300 per month including heat. Other utilities will be $275 per month. Other required costs are insurance at $3,500 per year. They will pay themselves $20 per hour (treat this as a variable cost). They will pay a sales commission (based on selling price) of 4% per complete set sold. Jack estimates that they can build 125 sets per year.




    i am asked to find....


    1. How many patio sets must they construct to break-even? Calculate the break-even point in:
    a. units.
    b. sales dollars.






    Thanks in advance..
    Selling Price: 3000 (given)

    Labour time (time per table + time per chair):
    25 + 4\cdot 10 = 65 \text{ hours}

    Materials per item (selling price-total cost)

    <br />
20 \cdot 12 + 10 + 15 + 4(12 \cdot 6 +6 + 10) +0.04 \cdot 3000 + 65 \times 20 = 2192 (edit: 20 should be 12 since each lumber is 12 not 20)



    Yearly Production = 125 (given)

    Other costs (Insurance + Storage + Rent)

    3500 + 275 \cdot 12 + 2300 \times 12 = 34400


    To break even Revenue = Loss

    3000n - (2192n + 34400) = 0

    Solve for n which is the number of units sold
    Last edited by e^(i*pi); June 9th 2010 at 12:00 PM. Reason: changing salary to be part of material cost
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2010
    Posts
    52


    can you tell me why you did this (4(20.6 + 6 +10)

    as well you treated wages as fixed cost...i am suppose to add to this Materials per item (selling price-total cost) aren't I?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by petedam View Post


    can you tell me why you did this (4(20.6 + 6 +10)

    as well you treated wages as fixed cost...i am suppose to add to this Materials per item (selling price-total cost) aren't I?
    Yes you're right, I changed this in hindsight. The 4(20*6+6+10) is the cost of the chairs. Each chair costs 20*6+6+10 and there are 4 of them
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    May 2010
    Posts
    43
    Given what you've been asked, essentially all costs are variable except rent, insurance and utilities, since they will be relatively fixed regardless of the units produced -- although in long term, all these costs mentioned are not really fixed (you can cancel insurance, and end your lease, quite easily as compared to owning a facility).

    The other costs are variable because they scale with the production. So find the level of production needed to cover the above costs.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jun 2010
    Posts
    52
    according to your revenue equation....i got an n value 0f 0.02241...it doesnt make sense.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by e^(i*pi) View Post
    To break even Revenue = Loss

    3000n - (2192n + 34400) = 0

    Solve for n which is the number of units sold
    Quote Originally Posted by petedam View Post
    according to your revenue equation....i got an n value 0f 0.02241...it doesnt make sense.
    I get an answer of 42.57

    n = \frac{34400}{3000-2192} \approx 42.57

    I attach an excel file for you to look at if you wish (it has the same info on, nothing new). It's just be easier to chop around the numbers


    nb: it should be safe but since I use linux I can't be sure that it's totally safe.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Jun 2010
    Posts
    52
    Quote Originally Posted by e^(i*pi) View Post
    I get an answer of 42.57

    n = \frac{34400}{3000-2192} \approx 42.57

    I attach an excel file for you to look at if you wish (it has the same info on, nothing new). It's just be easier to chop around the numbers


    nb: it should be safe but since I use linux I can't be sure that it's totally safe.

    sorry....i am an idiot and can't solve for n.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Jun 2010
    Posts
    52
    (edit: 20 should be 12 since each lumber is 12 not 20)

    shouldn't it be 2037?

    Because there are two of them should it be (65 x 20) x 2? for labour



    Again thanks a bunch!
    Last edited by petedam; June 11th 2010 at 07:46 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. break even point
    Posted in the Business Math Forum
    Replies: 1
    Last Post: March 31st 2010, 02:43 AM
  2. Break Even Point
    Posted in the Business Math Forum
    Replies: 2
    Last Post: October 19th 2009, 11:41 AM
  3. Break even point
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 16th 2008, 12:33 PM
  4. Break even point
    Posted in the Business Math Forum
    Replies: 0
    Last Post: March 22nd 2008, 10:01 AM
  5. Help needed with break point/change point models.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 4th 2007, 04:41 AM

Search Tags


/mathhelpforum @mathhelpforum