$2.$ The Falcon Heavy uses two additional Falcon $9$ first stages as strap$-$on boosters for the core booster $($Falcon $9$ w$/2$ stages in Q$1)$

Assume the boosters have additional $3$ MT of inert mass due to the need for aerodynamic fairings and other modifications. Assume that the Falcon Heavy must reach the same $\backslash (\backslash$Delta V $\backslash )$ as previously calculated.

a$)$ If all $3$ modules burn together, what is the payload to orbit?

b$)$ If the center core burns at $\backslash (70\backslash \%\backslash )$ while the boosters are burning, and the remaining fuel in the core is burned after jettisoning the boosters, what is the payload mass?

c$)$ Imagine now that the propellant tanks of the boosters also supply the engines in the booster core until booster depletion. At that point, the boosters will be jettisoned and the fully fueled center module will continue to burn. What is the payload then?