$($a$)$ Using the appropriate diagram$($s$),$ describe how an individual's choice between consumption and savings is determined. $[30$ marks$]$

$($b$)$ Within this context, are savings an increasing function of the interest rate? Explain your answer. $[30$ marks$]$

$($c$)$ Outline possible limitations of the above framework and discuss briefly how they might be addressed. $[40$ marks$]$ please draw the graphs too please