Cost-Volume-Profit (CVP) Analysis for Multi-Product Companies with Constraints: A manufacturing company produces three products, Product X, Product Y, and Product Z. The selling prices and variable costs per unit for each product are as follows:

Product X: Selling price $50, variable cost $30

Product Y: Selling price $60, variable cost $40

Product Z: Selling price $70, variable cost $50

The company has a production capacity constraint of 10,000 units for Product X, 8,000 units for Product Y, and 5,000 units for Product Z. Determine the optimal sales mix that maximizes the company's total contribution margin. Discuss how this analysis guides product pricing and production decisions.