Question $1-$

Nadia has $$20$ per week to spend on any combination of pineapples and green tea. The price of a pineapple is $$4$ and the price of a bottle of green tea is $$2.$ The table below shows Nadia's utility values. Use the table to answer the questions that follow the table.

$\backslash$table$[[\backslash$table$[[$Quantity$],[$of$],[$Pineapples$]],\backslash$table$[[$Total$],[$Utility$]],\backslash$table$[[$Marginal$],[$Utility$]],\backslash$table$[[$Marginal$],[$Utility per$],[$Dollar$]],\backslash$table$[[$Quantity$],[$of Green$],[$Tea$]],\backslash$table$[[$Total$],[$Utility$]],\backslash$table$[[$Marginal$],[$Utility$]],\backslash$table$[[$Marginal$],[$Utility per$],[$Dollar$]]],[1,32,-,-,1,28,-,-],[2,52,20,5,2,46,18,9],[3,64,12,3,3,54,8,4],[4,68,4,1,4,60,6,3],[5,70,2,0\mathrm{.}5,5,64,4,2],[6,71,1,0\mathrm{.}25,6,66,2,1],[7,71,0,0,7,67,1,0\mathrm{.}5]]$

a$.$ Complete the table by filling in the blank spaces.

b$.$ Suppose Nadia purchases $4$ pineapples and $2$ bottles of green tea. Is she consuming the optimal consumption bundle? If so$,$ explain why. If not, what combination should he buy and why?