Homer Simpson's utility depends on beer and pork chops in the following fashion u$($b$,$ c$)=4$

$($a$)$ What is the general expression for MRScb$?$ What is MRScb at $(9,10)?$ And at $(9,20)?$

$($b$)$ Which good has no impact on the value of MRScb$?$ What does this imply for the shape of indi$$erence curves?

$($c$)$ If Homer is initially consuming $9$ units of beer and $20$ units of pork chops, then what is the largest number of pork chops that he would be willing to give up in return for an additional $27$ units of beer?