Last year, a battery manufacturing company in Toronto incurred a loss of $$772,000\mathrm{.}00$ by producing and selling $42,000$ batteries. If their total revenue for the year was $$15,800,000\mathrm{.}00$ and the break$-$even volume of the plant is $56,700$ batteries, calculate:

a$.$ The selling price of each battery

Round to the nearest cent

b$.$ The variable costs for each battery

Round to the nearest cent