This problem is an idealized simplification of real$-$world problems to illustrate the use of quantitative reasoning and the strategic content of performance metrics.

Assume the following information about firm XYZ$.$

Annual days of operations: $360$ days.

Annual sales $ $2,500,000$

Markup: $15\%$

All operational capital is borrowed @ $40\%$ annual interest.

$1($a$)$ Beginning of the year inventory is worth $$250,000$ and end$-$of$-$the$-$year inventory $$300,000.$

$($i$)$ One average how long does it take to sell a piece of inventory?