Question $6$

$(5$ points$)$ Suppose that a consumer views plain yogurt, $\backslash ($ q$\_\{1\}\backslash ),$ and Greek yogurt, $\backslash ($ q$\_\{2\}\backslash ),$ as perfect substitutes. Given that Greek yogurt is thicker, creamier, and more concentrated, the consumer typically uses about $\backslash (2/3\backslash )$ cup of Greek yogurt for every $1$ cup of plain yogurt. The consumer also knows that the average price for a $32-$ounce container of plain yogurt is $\backslash (\backslash$$ $3\backslash ),$ while the $32-$ounce container of Greek yogurt costs $\backslash (\backslash$$ $4\backslash ).$ Given this information, select the correct statement.

$($a$)$ The consumer will buy $\backslash (\backslash$frac$\{$Y$\}\{4\}\backslash )$ containers of Greek yogurt.

$($b$)$ The consumer will buy $\backslash (\backslash$frac$\{$Y$\}\{4\}\backslash )$ containers of plain yogurt.

$($c$)$ The consumer will buy $\backslash (\backslash$frac$\{\backslash$gamma$\}\{3\}\backslash )$ containers of plain yogurt.

$($d$)$ The consumer will buy between $0$ and $\backslash (\backslash$frac$\{\backslash$gamma$\}\{4\}\backslash )$ containers of Greek yogurt.

$($e$)$ There is not enough information to determine the exact number of containers the consumer will buy.