Henderson Furniture sells reproductions of $18$th century furniture. For a particular table, the assumptions of the inventory model with backorders are valid.

D $=260$ tables per year

I $=25\%$ per year

C $=$ $$860$ per table

Co $=$ $$90$ per order

Cb $=$ $$50$ per table per year

The store is open $250$ days a year.

$($a$)$

What order quantity will minimize total cost? $($Round your answer to three decimal places.$)$

What number of planned backorders is associated with the minimum total cost? $($Round your answer to three decimal places.$)$

$($b$)$

What is the maximum inventory? $($Round your answer to two decimal places.$)$

$($c$)$

What is the cycle time $($in days$)?($Round your answer to two decimal places.$)$

days

$($d$)$

What is total cost $($$$)?($Round your answer to two decimal places.$)$