Arley$$s Bakery makes fat$-$free cookies that cost $$1\mathrm{.}20$ each. Arley expects $20\%$ of the cookies to fall apart and break. Assume that Arley can sell the broken cookies for $$1\mathrm{.}10$ each. Arley wants a $50\%$ markup on cost and produces $180$ cookies. What price should Arley charge for each unbroken cookie?

Note: Round your answer to the nearest cent.