## May 17, 2018

### Expanding The Assortment

You have a line of widgets, and they sell really well. A million dollars last year.

So you decide to expand ... you offer a cousin of widgets ... bidgets!
• Widget Sales drop from \$1,000,000 to \$800,000.
• Bidget Sales are \$500,000.
• Total Sales = \$1,300,000.
You're frustrated a bit that widgets seem to be "dying", so you introduce quidgets!
• Widget Sales drop from \$800,000 to \$700,000.
• Bidget Sales drop from \$500,000 to \$400,000.
• Quidget Sales are \$400,000.
• Total Sales = \$1,500,000.
Here's another fun way to look at the dynamic.
• 0 Product Lines = \$0.
• 1 Product Line = \$1,000,000.
• 2 Product Lines = \$1,300,000.
• 3 Product Lines = \$1,500,000.
Transformed into an index gets us to this:
• 0.000 , 0.000.
• 0.333 , 0.667.
• 0.667 , 0.867.
• 1.000 , 1.000.
Guess what? That's another situation where a*(x^b) comes into play!!
• a = 1.009.
• b = 0.387.
And just like that, we have a forecasting tool to help us figure out how big or small our merchandising assortment needs to be!