Percy prepares vegetable curry $($liquid$)$ in a pressure cooker. If the raw potatoes are $P,$ the raw tomatoes are $T,$ the raw onions are $O,$ and the cooked meal is $M,$ then $2P+T+O3M$ may represent the cooking process. Sometime during the process, Manu opens the lid and checks the curry to find that the potatoes are half$-$cooked $($take $x_P=0\mathrm{.}5).$ Volume of the cooker is $5L$ and $C_{P{O}_0}=C_{T_0}=C_{O0}=1\mathrm{.}5.$

a$.$ Determine the type of reactor to use as a model, and justify.

b$.$ Derive the reactor equation using $x_T,$ the conversion of tomatoes, as the basis.

c$.$ Derive the equation for $C_M,$ the final concentration of the meal.