Arilya enterprises is a fancy boutique store that sells men's and boys' shirts. They sell three times the number of men's shirts as boys' shirts. The average selling price for a man's shirt is $$80$ and that of a boy's shirt is $$45.$ The variable costs for men's shirts and boy's shirts are $$15$ and $$10$ each, respectively. The total fixed costs of the operation are $$276,000.$

$(1)$ Compute the volume of men's shirts and boys' shirts at the break$-$ even point.

$(2)$ How many men's shirts and boys' shirts would have to be sold to make a profit of $$1,656,000$ at the same mix?