Question

Andrews Sporting Goods, Inc., produces and sells children's softball mitts: vinyl mitts and basic leather mitts. Last year, Andrews sold 13,620 vinyl mitts and 4,540 leather mitts. Information on the two products is as follows:

Line Item Description Vinyl Mitts Leather Mitts
Price $7.50 $24.70
Variable cost per unit 3.80 14.60

Total fixed cost is $76,320.

Required: (Round break-even packages to four significant digits and break-even units to the nearest whole unit.)

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1. What is the sales mix of vinyl mitts and leather mitts?

5:2 1:2 2:1 4:1 3:2 3:1 3:1

2. Compute the break-even quantity of each product.

The break-even quantity for vinyl mitts is:

The break-even quantity for leather mitts is:

Answer 1

To calculate the sales mix of vinyl mitts and leather mitts, divide the total number of units sold for each product by the sum of units sold for both products. The break-even quantity for each product can be calculated by dividing the total fixed cost by the contribution margin per unit.

Step-by-step explanation:

To calculate the sales mix of vinyl mitts and leather mitts, we need to determine the proportion of sales for each product. In this case, the sales mix is determined by dividing the total number of units sold for each product by the sum of units sold for both products.

The break-even quantity for vinyl mitts can be calculated by dividing the total fixed cost by the contribution margin per unit, which is the difference between the selling price and the variable cost per unit of the vinyl mitts. The break-even quantity for leather mitts can be calculated in the same way.

Answer 2

The sales mix of vinyl mitts and leather mitts is approximately 5:5. The break-even quantity for vinyl mitts is 20,657 units and for leather mitts is 7,564 units.

Step-by-step explanation:

To calculate the sales mix of vinyl mitts and leather mitts, we need to calculate the total sales revenue for each product and then divide it by the total sales revenue for both products. The sales revenue for vinyl mitts can be calculated by multiplying the number sold (13,620) by the price ($7.50), which gives us $102,150. The sales revenue for leather mitts is calculated by multiplying the number sold (4,540) by the price ($24.70), which gives us $112,058. The total sales revenue for both products is $214,208. To find the sales mix, we divide the individual sales revenue by the total sales revenue. The sales mix for vinyl mitts is $102,150/$214,208 = 0.4777 or 47.77%. The sales mix for leather mitts is $112,058/$214,208 = 0.5223 or 52.23%. Therefore, the sales mix of vinyl mitts and leather mitts is 48:52 or approximately 5:5.

To compute the break-even quantity for each product, we need to first calculate the contribution margin per unit for each product. The contribution margin per unit is calculated by subtracting the variable cost per unit from the selling price per unit. For vinyl mitts, the contribution margin per unit is $7.50 - $3.80 = $3.70. For leather mitts, the contribution margin per unit is $24.70 - $14.60 = $10.10. Next, we divide the total fixed costs ($76,320) by the contribution margin per unit for each product to find the break-even quantity. The break-even quantity for vinyl mitts is $76,320/$3.70 = 20,657 units. The break-even quantity for leather mitts is $76,320/$10.10 = 7,564 units.