Question

A firm sells two products: normal grills and deluxe grills.

Normal grills sell for a per unit price of $250. Normal grill variable cost per unit is $150.

Deluxe grills sell for a per unit price of $400. Deluxe grill variable cost per unit is $350.

The firm has a sales mix of 2 normal grills for every 5 deluxe grills. That is, the sales mix is 2:5.

The firm has total fixed costs of $250,000.

How many unit sales of deluxe grills are required to earn a profit of $2,000,000?

Answers:	a. 5,000 units
	b. 75,000 units
	c. 25,000 units
	d. 15,000 units

Answer 1

	Normal grills	Deluxe grills
Selling price per unit	$250	$400
Variable costs per unit	$150	$350
Contribution margin per unit	$100	$50

Weighted average unit contribution margin = (Normal grills Contribution margin per unit * Sales mix) + (Deluxe grills Contribution margin per unit * Sales mix)

= ($100 * 2/7) + ($50 * 5/7)

= $28.57 + $35.71

= $64.28

Total units to be sold = (Fixed costs + Target profit) / Weighted average unit contribution margin

= ($250,000 + $2,000,000) / $64.28

= 35,003 units

Deluxe grills to be sold = 35,003 units * Sales mix

= 35,003 * 5 / 7

= 25,002 units

= 25,000 units (difference is due to rounding off)