# Math Help - Break even point

1. ## 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.

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

2. Originally Posted by petedam
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.

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

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)

$
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

3. 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?

4. Originally Posted by petedam

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

5. 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.

6. according to your revenue equation....i got an n value 0f 0.02241...it doesnt make sense.

7. Originally Posted by e^(i*pi)
To break even Revenue = Loss

$3000n - (2192n + 34400) = 0$

Solve for n which is the number of units sold
Originally Posted by petedam
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.

8. Originally Posted by e^(i*pi)
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.

9. (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!