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Sarah spends $$120$ a year on movie tickets and ice cream. The table below shows her utility from each good. The price of a movie ticket is $$5$ and the price of ice cream is $$5$ per gallon

a$)$ Complete the table$-(2$ marks$)$

$\backslash$table$[[\backslash$table$[[$Quantity$],[($movies per$],[$year$)]],\backslash$table$[[$TU from$],[$movies$]],\backslash$table$[[$MU from$],[$movies$]],\backslash$table$[[($MU$/$P$)$ for$],[$movies$]],\backslash$table$[[$Quantity$],[($gallons of$],[$ice cream per$],[$year$)]],\backslash$table$[[$TU from ice$],[$cream$]],\backslash$table$[[$MU for$],[$ice cream$]],\backslash$table$[[($MU$/$P$)],[$for ice$],[$cream$]]],[0,0,,0,0,,,],[4,80,,4,120,,,],[8,152,,8,224,,,],[12,216,,12,312,,,],[16,272,,16,384,,,],[20,320,,20,440,,,],[,,,,,,,]]$

b$)$ Conclude whether or not Sarrah follow the law of diminishing MU$-(1\mathrm{.}5$ marks$)$

c$)$ What is your optimal combination of movies and ice cream?$-(3$ marks$)$

d$)$ Draw the Iotal utility $($TU$)$ and Marginal Utility $($MU$)$ for movies and then conclude$-(2$ marks$)$