$(40$ points$)$ The tubing assembly shown has a bottom portion of brass $(C83400)$ and a top portion of low$-$density polyethylene $($LDPE$).$ The accompanying plot shows the tensile stress$-$strain response of three different LDPE specimens. Both tubes have an outer diameter of $20$ mm $.$ The brass tube has a wall thickness of $1$ mm and the LDPE tube has a wall thickness of $2$ mm $.$

$($a$)$ What is the approximate yield stress of LDPE, indicated by the upper yield point on the plot?

$($b$)$ Based on the plot, estimate the elastic modulus of LDPE.

$($c$)$ If point A displaces $1$ mm under the applied loads shown in the image, calculate the length of the LDPE tubing $(2$L$).$