A pen manufacturer makes luxury pens. The pen case costs $$7\mathrm{.}26$ each, the ink holder costs $$1\mathrm{.}26$ each, the spring costs $$\mathrm{.}07$ each and the velvet pen case costs $$0\mathrm{.}91$ each. The plant has general and administrative costs of $$55000$ and fixed selling expenses of $$37500.$ The pens sell of $$39\mathrm{.}95$ each. Plant capacity is $4000$ pens per period. $(10$ points$)$

a$.$ At what percentage of capacity is the break$-$even point?

b$.$ If the manufacturer wants to make $$2000$ profit per period, what is the price they should charge if they work at full capacity?

c$.$ Suppose the price of each pen drops to $$25.$ How much should the manufacturer reduce their fixed cost to break$-$even at the same quantity as part $($a$)?$