Need formula for tier pricing and discounts

[stuartlujan]

Hi everyone,
My Name is Stuart Lujan. I am looking for some help from math experts! I print and sell vinyl banners and wallpaper but I sell them by square feet. I want to find a formula that allows me to price these items better, for example.

First, my base price for a banner is $2.5 square feet.
if the client needs a banner 4ft x 6ft = 24ft the price will be (24 x 2.5) - $60
now if they want to order more banners instead of only one, the price per square feet will be less.
let say they need 50 banners 4ft x 6ft then the price per sq ft will be $1.75

Second, the material that I use for each item that I sell comes in different roll sizes. I need to keep in count the waste material.
so if a client needs to print a vinyl wrap (wrap vinyl comes in rolls of - 54 inch wide by 150ft long)
if the print is 34 inch wide by 60 inch long (then I have to print it by the shortest side that fits in 54" so I waste 10 inches on each sides x 60 inches long = 8.33 sq ft waste)

I am looking for a formula that keeps all these things in mind.
so I can just input the print size the client needs and the formula can do all the calculations including the waste, and quantity the more they order the lower the price per square feet.

I know you math geniuses have an idea how to do this, I only sell vinyl and this math is driving me crazy.
please let me know if you have any questions.

 

[Steven G]

First I want to say that just like 5x5 is not 5, ft x ft is not ft. That is 4ft x 6ft = 24ft is not correct. 4ft x 6ft = 24ft²

I really am not sure what the problem is. You seem to have it all worked out.

When your roll is 54 inch wide, you need to charge by the length. That is if someone wants 45in x 5ft you have to charge for 5 feet. You might want to charge even more since you have to cut the width, but that is your decision.

For each type of roll you sell you need to list the price for a length of 0in to ?ft and from ?ft to ??ft and from ??ft to ???ft ...

 

[Dr.Peterson]

I am looking for a formula that keeps all these things in mind.
so I can just input the print size the client needs and the formula can do all the calculations including the waste, and quantity the more they order the lower the price per square feet.

I agree with Jomo on the length aspect.

As for the quantity discount, that too is a decision you have to make. How did you choose to reduce the price from $2.50 per sq. ft. to $1.75 per sq. ft. for a quantity of 50? What would it be for other quantities? Once you describe a rule, we could put it into a formula (or suggest a change that would make a formula simpler).

 

[stuartlujan]

Hi, first thank you for taking the time to answer.
like I said before most of my rolls come in 54" w x 150' L
so my minimum print size is 4.5 sq ft. (this is because of the amount of waste on tiny prints)
the max price is $2.50 per sq ft

the more the client orders the less the sq ft price gets.
the minimum price is $.99 per sq ft (from 200 sq ft and up)

so from 4.5 sq ft until 35 sqft, my price will be $2.5 sq ft
after that, it can gradually go down let's say 10% every 10sqft until it reaches 200sqft at $.99 per sq ft.

also, I need to keep in mind the waste material.
example: if I have to print a 38" X 68" image (17.944 sq ft) - I will use 54" X 72" of a roll (27 sq ft) so I will have 9 sq ft waste.
I would like to calculate the waste at $.65 sq ft

so I need that in a formula that I can plug the size of the image I need to print and It can give me the correct price.
see attachment to see if that can help you understand what I mean.
I am willing to compensate you for your time. I really need this formula to create a website and help my sales team.

 

[Steven G]

I think you do not understand sq ft. But you do not have to. You sell by the length which is linear. That means you sell by the in or by the ft or by the yd. If the width your customer wants is less than the width of your roll then you cut it and have waste. But still you price it by the length they want. Is this clear?

Why on earth if a customer wants a print size of 38" X 68" would you use 54" X 72". There must be something we are missing that maybe you did not tell us. If the roll is 150 ft long why don't you cut off a piece that is exactly 68" instead of 72". Why lose the 4" by 54" piece of material??

 

[Dr.Peterson]

I'll focus on the quantity discount issue while Jomo pays attention to the area vs length and wastage issues.

so my minimum print size is 4.5 sq ft. (this is because of the amount of waste on tiny prints)
the max price is $2.50 per sq ft

the more the client orders the less the sq ft price gets.
the minimum price is $.99 per sq ft (from 200 sq ft and up)

so from 4.5 sq ft until 35 sqft, my price will be $2.5 sq ft
after that, it can gradually go down let's say 10% every 10sqft until it reaches 200sqft at $.99 per sq ft.

If it went down 10% for every 10 sq.ft., then (assuming you really mean percent, not just 10% of 2.50) the prices would be
0-35: $2.50
35-45: $2.25
45-55: $2.03
55-65: $1.82
65-75: $1.64
75-85: $1.48
85-95: $1.33
95-105: $1.20
105-115: $1.08
115-125: $0.97

and it's already gone below $0.99.

Did you have some reason to pick that rule, or was that just an example?

More curious, you originally seemed to be saying the discount wasn't for more feet, but for more pieces: "let say they need 50 banners 4ft x 6ft then the price per sq ft will be $1.75". That doesn't fit with what you say here, as this is far, far more than 200 sq.ft..

Are there any concrete reasons for particular choices of how fast the price would decrease? Is there any typical rule your competitors follow that you'd want to match?

 

[stuartlujan]

Good morning,
Jomo - in my industry we charge by the square footage - (WxL). The reason I use more material to print a 38X68 is that the machine requires about 2 to 3 inches on the top and at the bottom to be able to grab the paper when it moves it. That's the reason I use 72" long and 54" because that's the width of the roll.

Mr Peterson - the 10% was just an example - I did the calculation and the exact percentage will have to be 5%
0-35 - 2.50
35-45 - 2.38
45-5 - 2.26
55-65 - 2.14
65-75 - 2.04
75-85 - 1.93
85-95 - 1.84
95-105 - 1.75
105-115 - 1.66
115-125 - 1.58
125-135 - 1.50
135-145 - 1.42
145-155 - 1.35
155-165 - 1.28
165-175 - 1.22
175-185 - 1.16
185-195 - 1.10
195-199.9 - 1.05
200+ - 0.99

The particular choices of prices are due to competitors' prices I want to match.

the Width and the Lenght of the print area are very important because we charge by the square footage.
but the waste material plays a very big factor in calculating the pricing. for example.
if you get a client that needs to print one artwork of 11"X68"
I will only be able to fit one on the roll of 54" and will have 43" waste.
so my calculation are as follow:
print area = 11"x68" = 748 sq inch = 5.19 sqft x $2.5 (print price per sqft) = $12.98
waste area = 43"x68" = 2,924 sq inch = 20.13 sq ft = x $.65 (wast price per sqft) = $13.08
( I divide the total on sq inch by 144 to get the sq ft)
so One print will cost my client = $26.06

But, if the client needs 4 of the same print, then I can fit 4 on a 54" side. the smallest side of the print is 11" and the client needs 4 so 11" X 4 = 44" this means we only wast 10"
print area = 11"x68" = 748 sq inch x 4 (qty of prints) = 20.77 sqft x $2.5 (print price per sqft) = $51.75
waste area = 10"x68" = 680 sq inch = 4.72 sq ft = x $.65 (wast price per sqft) = $3.06
so this print will cost my client = $54.81
Here each print will cost = $13.70

 

[Steven G]

The total price then would be (square footage of the area ordered) * (price per square ft) + [ (54" * length ordered) - (square footage of the area ordered) ] * (wastage cost per square ft)

I guess that if someone orders 54" x 68" you need to cut a piece 54" x 72" and only charge them for 54" x 68" ??