A firm has two products, J and K$.$ Product J has a sales price of $$8$ and a variable cost per unit of $$5.$ Product K has a sales price of $$15$ and a variable cost per unit of $$10.$ The firm expects to sell these two products in a mix of $2$ units of Product J to $3$ units of Product K$.$

If the firm has $$100,000$ in fixed costs, how many units of Product J need to be produced and sold to earn $$900,000$ in profit?