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\begin{aligned}\frac{d}{d p_{s}}\left(\mathrm{ATP}_{1}\right) &=0 \\\Rightarrow p_{s} &=\frac{2 D_{R}-B \pm \sqrt{\left(2 t_{s}-A\right)^{2}-4\left(2 t_{s}-A\right)\left(E-B D_{R}\right)}}{2\left(2 t_{s}-A\right)}\end{aligned}