Question

Sales Mix and Break-Even SalesDragon Sports Inc. manufactures and sells two products, baseball bats and baseball gloves. The fixed costs are $620,000, and the sales mix is 40% bats and 60% gloves. The unit selling price and the unit variable cost for each product are as follows:Products Unit Selling Price Unit Variable CostBats $90 $50 Gloves 105 65 a. Compute the break-even sales (units) for the overall enterprise product, E.unitsb. How many units of each product, baseball bats and baseball gloves, would be sold at the break-even point?Baseball bats unitsBaseball gloves units

Answer 1

a. 15,500 units

b. 6,200 bats and 9,300 gloves

Step-by-step explanation:

Fixed costs (F)=$620.000

Sales mix=40% bats and 60% gloves

Selling price of bats (Sb) =$90

Variable cost of bats (Vb) =$50

Selling price of gloves(Sg) =$105

Variable cost of gloves (Vg)=$65

The average contribution (C) per unit can be determined as:

`C=0.4*(S_(b) - V_(b)) + 0.6* (S_(g) - V_(g)) \\C=0.4*(90 - 50) + 0.6* (105 - 65) \\C= \$ 40`

In order to reach the break-even point the total contribution of 'n' units must equal fixed costs:

`\$40 *n = \$620,000\\n=15,500 \ units`

Since we know the sales mix, the number of bats (B) and gloves (G) are:

`B= 15,500*0.4\\B=6,200\\G= 15,500*0.6\\G=9,300\\`

At the break-even point, 6,200 bats and 9,300 gloves would be sold.