Court Inc. produces two types of products - Gizmos and Gadgets. The following information is available related to each product: Gizmos Gadgets Sales price per unit $80 $50 Variable costs per unit 36 22 Three-fourths of the products sold are Gizmos and one-fourth are Gadgets (3:1). If total fixed costs are $50,000, how many total units need to be sold in order for the company to break even?

1250

Explanation:

Let's go in stages,

Gizmos are sold for $80 and have a variable cost of $36. Subtracting that would give us $44. This is the Contribution margin of Gizmos.

Gadgets are sold for $50 and have a variable cost of $22. Subtracting that would give us $28. This is the Contribution margin of Gadgets.

The text says that 3/4 of goods sold are Gizmos with the rest being gadgets.

Let's account for that using their contribution margins.

This means that Gizmos contribute 3/4 from their CM which we'll calculate as,

= 3/4 * 44

= 33

Gadgets would be

= 1/4 * 28

= 7

The Weighted Average contribution margin for both goods in their selling proportion is therefore,

= 33 + 7

= $40

If they make $40 as the weighted average CM then to find the amount of units needed to break even with a fixed cost of $50,000 can be calculated by dividing the fixed costs by the Weighted Average CM which would be,

= 50,000/40

= 1250

They would need to sell 1250 total units in order to break even with a product mix of 3/4 Gizmos and 1/4 Gadgets.

Please do react or comment if you need any clarification. Thank you.

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