Mike's restaurant sells a $10-$inch pizza for $$10.$ To save on costs and increase profits, Mike has decided to change the size of the pizza. He wants to keep the price the same $($$$10)$ but wants to reduce the size of the pizza. Importantly, he doesn't want people to realize the size is smaller. Market research tells him that the Just$-$Noticeable$-$Difference for pizza size is $0\mathrm{.}5$ inches. Based on this information, what should be the new pizza size?

$10$ inches $($No Change$)$

$10\mathrm{.}5$ inches

$0\mathrm{.}5$ inches

$9\mathrm{.}4$ inches

$9\mathrm{.}6$ inches