Question

Question was provided via image upload.

Explanation:

Calculate unit contribution margins

Using the Unit Contribution Margin knowledge point:

• For Bats:

$$ \text{UCM}_{\text{Bats}} = \$85 - \$50 = \$35 $$

• For Gloves:

$$ \text{UCM}_{\text{Gloves}} = \$60 - \$35 = \$25 $$

Compute weighted average contribution margin

Using the Sales Mix and Weighted Average Contribution Margin knowledge points:

• Sales mix is \(40\%\) Bats and \(60\%\) Gloves.

$$ \text{WACM} = (0.40 \times \$35) + (0.60 \times \$25) = \$14 + \$15 = \$29 $$

Determine overall break-even sales in units

Using the Break-Even Analysis knowledge point:

• Total fixed costs are \(\$1,450,000\).

$$ \text{Break-Even Units (Overall)} = \frac{\$1,450,000}{\$29} = 50,000 \text{ units} $$

Calculate break-even units for each product

Using the Sales Mix knowledge point:

• Baseball bats:

$$ 50,000 \times 0.40 = 20,000 \text{ units} $$

• Baseball gloves:

$$ 50,000 \times 0.60 = 30,000 \text{ units} $$

Answer:

Question a

Compute the break-even sales (units) for the overall company's mix of product, \(E\):
<blank>50,000</blank> units

Question b

How many units of each product, baseball bats and baseball gloves, would be sold at the break-even point?
Baseball bats: <blank>20,000</blank> units
Baseball gloves: <blank>30,000</blank> units