Tabitha manufactures a product that sells very well. The capacity of her facility is $267,000$ units per year. The fixed costs are $$126,000$ per year and the variable costs are $$11$ per unit. The product currently sells for $$19.$

a$.$ What total revenue is required for a net income of $$429,000$ per year?

Round to the nearest cent

b$.$ If sales were at $55\%$ of the capacity and the variable costs decreased by $25\%,$ what would be the net income per year?

Round to the nearest cent