Variable	N
Variable	$0 < N < \frac{27 k^{2} θ^{3}}{1024 β}$	$\frac{27 k^{2} θ^{3}}{1024 β} \leq N < \frac{k^{2} θ^{3}}{36 β}$
$p^{*}$	$\frac{θ}{β} - {(\frac{2 N}{k^{2} β^{2}})}^{1 / 3}$	$\frac{5 θ}{8 β}$
$a^{*}$	${(\frac{N^{2}}{2 k β})}^{2 / 3}$	$\frac{81 k^{2} θ^{4}}{16384 β^{2}}$
$w^{*}$	$\frac{θ}{β} - 2^{4 / 3} {(\frac{N}{k^{2} β^{2}})}^{1 / 3}$	$\frac{θ}{4 β}$
$t^{*}$		0
$D^{*}$	N	$\frac{27 k^{2} θ^{3}}{1024 β}$
$π_{m}^{*}$	$\frac{N θ}{β} - 4 {(\frac{N^{2}}{2 k β})}^{2 / 3}$	$\frac{27 k^{2} θ^{4}}{4096 β^{2}}$
$π_{r}^{*}$	${(\frac{N^{2}}{2 k β})}^{2 / 3}$	$\frac{81 k^{2} θ^{4}}{16384 β^{2}}$
$π_{m + r}^{*}$	$\frac{N θ}{β} - 3 {(\frac{N^{2}}{2 k β})}^{2 / 3}$	$\frac{189 k^{2} θ^{4}}{16384 β^{2}}$