Consider a system with $4$ types of resources: A$,$ B$,$ C$,$ and D$.$ The maximum resources that can

be allocated to each process and the current allocation are as follows:

$$ Maximum Resources:

$$ Process P$1$: A$=7,$ B$=5,$ C$=3,$ D$=6$

$$ Process P$2$: A$=3,$ B$=2,$ C$=2,$ D$=5$

$$ Process P$3$: A$=9,$ B$=0,$ C$=2,$ D$=7$

$$ Currently Allocated Resources:

$$ Process P$1$: A$=0,$ B$=1,$ C$=0,$ D$=4$

$$ Process P$2$: A$=2,$ B$=0,$ C$=0,$ D$=0$

$$ Process P$3$: A$=3,$ B$=0,$ C$=2,$ D$=2$

Assume the system has $15$ units of each resource available initially. Use the Banker's Algorithm to answer the following questions:

$1.$ Is the system in a safe state initially? If yes, provide a safe sequence. If no$,$ explain why not.

$2.$ If Process P$2$ requests resources A$=1,$ B$=1,$ C$=1,$ D$=1,$ can the request be granted immediately? Explain your answer.

$3.$ If Process P$3$ requests resources A$=3,$ B$=0,$ C$=0,$ D$=3,$ can the request be granted immediately? Explain your answer.