A firm is selling two products, chairs and bar stools, each at \(50 per unit. Chairs have a variable cost of \)25, and bar stools \(20. Fixed cost for the firm is \)20,000.

a.If the sales mix is 1:1 (one chair sold for every bar stool sold), what is the break-even point in dollars of sales? In units of chairs and bar stools?

b.If the sales mix changes to 1:4 (one chair sold for every four bar stools sold), what is the break-even point in dollars of sales? In units of chairs and bar stools?

ABreak-even pointis that point in the production process where the firm earns neither loss nor profit. At this point, the total revenue from the sale and the total cost of production equate to each other.

Break-even point (dollars) = Total fixed costs / [(weighted average selling price -

weighted average variable expense)/ weighted average selling price]

Weighted average selling price = (selling price x weighted sales participation) = $50

Weighted average variable cost = (variable cost x weighted sales participation)

Weighted average variable cost = (25 x 0.5 + 20 x 0.50) = $22.5

Break-even point in dollars (BEP) = 20,000/ [(50 - 22.5)/ 50] = $36,364

Revenue = 50 x 5 = 250

Combined VC = (20 x 4) +25 =105

BEP = 20000/ (250-105) = 138 (rounded)

Sales = 137.93 x 250 = 34,500 (rounded)

Chairs = 138

Bar stools = 138 x 4 = 552 (rounded)