Question

Pure Water Products produces two types of water filters. One attaches to the faucet and cleans all water
that passes through the faucet. The other is a pitcher-filter that only purifies water meant for drinking.
Revenue and cost information for each product appears below:

●      the unit that attaches to the faucet is sold for $70 and has variable costs of $30

●     the pitcher-filter sells for $80 and has variable costs of $45

●     fixed costs total $424,000

●     Pure Water sells 4 faucet models for every 3 pitcher-filters sold

Calculate the number of units of the faucet-model that must be sold in order for Pure Water Products
to earn a target profit of $212,000.

Answer 1

Solution:

Computation of weighted average contribution margin per unit
Particulars	Faucet	Pitcher Filter	Total
Selling price per unit	70	80
Variable cost per unit	30	45
Contribution margin per unit	40	35
Sales mix	4/7	3/7
Weighted average contribution margin per unit	22.8571	15.0000	37.8571

Nos of units to be sold to earn target profit = (Fixed costs + Target profit) / Weighted average contribution margin per unit

= ($424,000 + $212,000) / 37.8571 = 16800 units

Nos of units of the faucet model to be sold to earn target profit = 16800*4/7= 9600 units