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Math in the fashion design industry (PRICING (Example (Cost per dress = …
Math in the fashion design industry
PRICING
LOGS AND EXPONENTS
:
To work out the minimum viable order size, you examine your production costs.
Cost per dress = 50 / exp(0.0002 × n) + 50
where n is the number of dresses in the order and ‘exp’ is the exponential function.
Example
Cost per dress = 50 / exp(0.0002 × n) + 50
Cost per dress – 50 = 50 / exp(0.0002 × n)
exp(0.0002 × n) × (Cost per dress – 50) = 50
exp(0.0002 × n) = 50 / (Cost per dress – 50)
Take the natural log ln of both sides:
ln[exp(0.0002 × n)] = ln[50 / (Cost per dress – 50)]
0.0002n = ln[50 / (Cost per dress – 50)]
n = ln[50 / (Cost per dress – 50)] / 0.0002
Substitute in the maximum allowable cost per dress:
n = ln[50 / (60 – 50)] / 0.0002
n = 8047 dresses
RUNWAY TRAFFIC
Every designer needs a fashion show to display their products
They have to calculate the time each outfit can be modelled for according to the total time of the show
EXAMPLE:
time: 35 mins 2 mins for musical performances and 4 mins for the final walk with all the models and the designer.
Number of outfits = 40.5
Number of outfits = (35 – 2 × 4) / 0.6667
Number of outfits = time available / time per catwalk
OPTIMISING PRODUCTION PROCESSES
Although you only needed to buy an approximate amount of fabric for the prototype gowns, for mass production your designers will need to work out exactly how much fabric they need per clothing item.
EXPANDING YOUR DESIGNER TEAM
After a designer creates a really big business they can't design every piece themselves so they chose people to design for them.
These designers get a salary, a yearly bonus plus equity in the company.
EXAMPLE
Cash available per designer = increased profit × profit percentage usable / number of new designers
Cash available per designer = 12500000 × 0.2 / 5
Cash available per designer = $500000
Half a million dollars – that should be attractive. But we’ve still got to divide it up into salary and bonus:
Total cash package = salary + bonus
The bonus has to be 20% of the base salary, so bonus = 0.2 × salary:
Total cash package = salary + bonus
Total cash package = salary + 0.2 × salary
Total cash package = 1.2 × salary
salary = total cash package / 1.2
salary = 500000 / 1.2
salary = $416667
And:
bonus = 0.2 × 416667
bonus = $83333
