(i) Demand slope $=\underline{570-820}=-1.25$

$400-200$ Equation of demand

$\frac{P-570}{q-400}=-1.25$

$P=-1.25(q-400)+570=-1.25 q+1070$

Revenue, $R=(1070-1.25 q) q=1070 q-1.25 q^{2}$

(ii) Total cost, $\mathrm{TC}=\int(2 \mathrm{q}-570) \mathrm{dq}$

$=q^{2}-570 q+C$

$C=$ fixed cost $=1,100$

$T C=q^{2}-570 q+1,100$

(iii) Profit, $\pi=1070 q-1.25 q^{2}-q^{2}+570 q-1100$

$=-2.25 q^{2}+1640 q-1100$

At B.E.P, profit $=0 \Rightarrow \Rightarrow-2.25 q^{2}+1640 q-1100=0$

$q=-1640 \pm \sqrt{1640^{2}}-4(-2.25)(-1100)$

$2(-2.25)$

$q=0.67$ or $q=728$

(iv) $P=1070-1.25 q$

$\underline{\mathrm{d} p}=-1.25 \mathrm{pdq}=\frac{1}{\mathrm{dp}}=-0.8$

$\mathrm{dq} \quad$ When $\mathrm{q}=110, \mathrm{p}=932.5$

Point of elasticity, $\mathrm{E}=\mathrm{p} \times \underline{\mathrm{d}} \underline{\mathrm{p}}$

$\begin{array}{ll}q & d p \\ = & \quad \underline{932.5} \times-0.8\end{array}$

$=-6.78$