Champion Cooling has just signed a contract to rooftop air conditioners for another company. The list of tasks, including time requirements and immediate predecessors, follows. Each task may not be shortened. They plan to make $32$ units in an eight$-$hour day. What is the theoretical minimum number of stations?

Task

Bolt compressor to base

Install coils and lines

Install fan motor

Install switch and thermostat

Charge system and test

Cosmetic detailing

$1$

Time $($min$)$

$5$

$6$

$7$

$5$

$10$

$7$

Predecessor

None

Bolt compressor to base

Install coils and lines

Install fan motor

Install switch and thermostat

Charge system and test