Gorge Mfg. produces two products, X and Y. The following information is presented for both products:

X Y
Selling price per unit $9 $6
Variable cost per unit $7 $3

Total fixed costs are $117,000.

What will the breakeven point be for Gorge in units of X and Y if the ratio of sales is expected to be 3X:2Y?

Question

Gorge Mfg. produces two products, X and Y. The following information is presented for both products:

X	Y
Selling price per unit	$9	$6
Variable cost per unit 	$7	$3

Total fixed costs are $117,000.

What will the breakeven point be for Gorge in units of X and Y if the ratio of sales is expected to be 3X:2Y?

BlackTom AI · Accepted Answer

Contribution margin per unit for X is $2 (9 − 7) and for Y is $3 (6 − 3).

1) Relevant knowledge points and concepts
- Contribution margin (CM) = Selling price − Variable cost.
- For a multi-product firm with a given sales mix, compute the CM for a representative "bundle" (composite unit) that reflects the sales ratio, then divide total fixed costs by the bundle CM to find break-even bundles. Alternatively, compute a weighted-average CM per unit across the mix.

2) Step-by-step reasoning
- Compute individual CMs:
  - CM_X = $9 − $7 = $2 per X
  - CM_Y = $6 − $3 = $3 per Y
- Sales mix: 3 X : 2 Y. Form a bundle of 3 X and 2 Y (total 5 units).

3) Intermediate calculations
- CM of one bundle = 3 × CM_X + 2 × CM_Y
  = 3 × $2 + 2 × $3
  = $6 + $6
  = $12 per bundle.
- Break-even number of bundles = Fixed costs / CM per bundle
  = $117,000 / $12
  = 9,750 bundles.
- Convert bundles to units:
  - X units = 3 × 9,750 = 29,250 units
  - Y units = 2 × 9,750 = 19,500 units

(Alternative check using weighted-average CM per unit: bundle has 5 units, so weighted CM per unit = $12/5 = $2.40. Total units to break even = $117,000 / $2.40 = 48,750 total units; X = 3/5 × 48,750 = 29,250; Y = 2/5 × 48,750 = 19,500 — same result.)

4) Why the correct answer is correct
The break-even point must cover fixed costs using the contribution provided by the actual sales mix. The bundle method correctly attributes contribution according to the 3:2 ratio; dividing fixed costs by the bundle contribution yields the number of bundles required, which when multiplied by the mix proportions yields the unit break-evens found above.

5) Why other options are incorrect
- The other numeric choices do not satisfy both the 3:2 sales mix and the required contribution to cover $117,000 fixed costs (they yield different total contributions or incorrect mix proportions).

6) Conclusion
The break-even units are X = 29,250 and Y = 19,500, which matches the provided answer.

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