$5.(10)($Ch$\mathrm{.}9,$ Price Discrimination$)$ A firm with costs C$($Q$)=1,000+60$Q $+0\mathrm{.}1$Q$2$ is able to pricediscriminate between two groups of customers, with demands Q$1=3,000-2$p$,$ and Q$2=3500\mathrm{.}5$p respectively. How much does it sell to each group, and at what price? What would happen if it were forced to charge all its customers the same price? $($Tip: for the second part of the question, get the sum of the two demand functions.