$1.$ Yerke Company makes jungle gyms and tree houses for children. For jungle gyms, the selling price is $$120$ and variable expenses are $$90$ per unit. For tree houses, the selling price is $$200$ and variable expenses are $$100.$ Fixed expenses are $$50,000$ for each product line and $$153,750$ for the company $($common$).$ Last year, Yerke sold $12,000$ jungle gyms and $4,000$ tree houses. This year, Yerke expects to sell $12,000$ jungle gyms and $8,000$ tree houses. Think about which would be a better sales mix to use. Using this sales mix, how many jungle gyms need to be sold to breakeven?

$2.$ Xeller Company makes electronic keyboards. The practice model price is $$220$ and variable expenses are $$190$ per unit. The deluxe model price is $$340$ and variable expenses are $$250$ per unit. The professional model price is $$1,200$ and variable expenses are $$800$ per unit. Total fixed expenses are $$187,000.$ Generally, Xeller sells $6$ practice models and $3$ deluxe models for each professional model sold. Based on the preceding sales mix, how many total keyboards must be sold to breakeven and how many of them are deluxe models?