$6.$ These are the tasks necessary for the final assembly of a hospital bed, the time needed to perform each task, and the operations that must be completed prior to subsequent operations. The time available is $00$ minutes per day, and the required output rate is $25$ beds per day.

Time $($min$)$ Immediate Predecessors

Task

A

$4$

None

B

$5$

None

C

$8$

None

D

$4$

A

$$

LL

E

$3$

A$,$B

F

$3$

B

G

$5$

D$,$E

H

$7$

F

$1$

$1$

G$,$H

#bA

J

$7$

K

$4$

C$,$J

a Construct