Calculate the free energy of mixing $(\frac{F_{\text{m}\text{i}\text{x}}}{k_B})$ for a polymer blend of SPB$/$dSPB where $N_A=$

$N_B=2,000$ at $305K,350K,$ and $400K.$ Assume $A=-9\mathrm{.}2{10}^{-4},B=0\mathrm{.}722,C=0$ and these

values apply in the range $T=30-130C.$ Include the $vs$ and $Tvs$ plots with the binodal

line as a solid line while the spinodal as a dashed line. Properly label the unstable spinodal,

metastable, and stable regions regions. Also, find ${}_c,{}_c,$ and $T_c.$ Pick the correct y$-$axis ranges to

show the data properly; otherwise, points will be taken.