A firm sells two products. Product R sells for $20; its variable cost is $6. Product S sells for $50; its variable cost is $30. Product R accounts for 60 percent of the firm's sales, while S accounts for 40 percent

The firm's fixed costs are $4 million annually. Calculate the firm's break-even point in dollars.

The contribution for product R is 70 percent of selling price, or 0.70; the contribution for product S is 0.40. The weighted contribution for R is .70 × .60 = .42; the weighted contribution for S is .40 × .40 = .16. The sum of the weighted contributions is 0.58. The break-even point is $4,000,000 / 0.58 = $6,896,552.