# Decreasing cost per square foot..?

#### Dave2433

##### New member
Hi All,

This is my first post so please forgive any posting protocol blunders I may make, the first one being that I don't know which topic heading to post this to.

My question is this, if I make a sign at 8ft x 4ft and charge £200 for it then that is at a rate of £6.25 per square foot, which is fine. But if I use that square foot rate to calculate the cost of a small door sign at say 1ft x 5ins it gives a price of £2.60 which is way too low as it should cost £15.40.

Conversely, if I use the new square foot rate calculated from the new cost of the small sign, which is now £36.96 and use that to calculate the cost of the 8ft x 4ft sign it works out to a ridiculously expensive £1,182.72.

It's obviously not a linear increment related to a standard value per square foot, but we all accept that the more you buy the cheaper each individual unit becomes. Can anyone help me derive a formula that allows a calculation that reduces cost per unit as the number of unit purchased increases?

I enjoy the odd mathematical puzzle but I'm not getting anywhere with this one......

#### stapel

##### Super Moderator
Staff member
My question is this, if I make a sign at 8ft x 4ft and charge £200 for it then that is at a rate of £6.25 per square foot, which is fine. But if I use that square foot rate to calculate the cost of a small door sign at say 1ft x 5ins it gives a price of £2.60 which is way too low as it should cost £15.40.
On what basis have you concluded that the smaller sign "should" cost the noted amount?

Conversely, if I use the new square foot rate calculated from the new cost of the small sign, which is now £36.96 and use that to calculate the cost of the 8ft x 4ft sign it works out to a ridiculously expensive £1,182.72.
On what basis have you concluded that the larger sign "should" cost a lower amount?

It's obviously not a linear increment related to a standard value per square foot, but we all accept that the more you buy the cheaper each individual unit becomes.
Sometimes. Not always. For instance, hardwood planks cost more per unit for larger pieces, probably because they come from larger trees, which cost more (in time, and thus in money) to grow (and are also less common than smaller trees).

Can anyone help me derive a formula that allows a calculation that reduces cost per unit as the number of unit purchased increases?
Sure. What sort of model have you been told to use (quadratic, cubic, exponential, etc), what method did they give you in class for finding the model (straight algebra, statistical regression, etc), and what other assumptions have they given you to apply?

We can help you with the math, but you'll need to provide all of the parameters (the faux "real world" stuff for this exercise).

When you reply, please include a clear listing of your thoughts and efforts so far, specifying where you're getting bogged down. Thank you! 