Heather Adams, production manager for a Colorado exercise equipment manufacturer, needs to schedule an order for $50$ UltimaSteppers, which are to be shipped in week $8.$ Subscripts indicate quantity required for each parent. Assume lot$-$for$-$lot ordering. Below is information about the steppers:

ITEM

LEAD TIME

ON$-$HAND INVENTORY

COMPONENTS

Stepper

$2$

$20$

A$(1),$ B$(3),$ C$(2)$

A

$1$

$10$

D$(1),$ F$(2)$

B

$2$

$30$

E$(1),$ F$(3)$

C

$3$

$10$

D$(2),$ E$(3)$

D

$1$

$15$

E

$2$

$5$

F

$2$

$20$

Develop a product structure for Heather.

Develop a time$-$phased structure.