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A business sells 3 products with the following information.Product Sales Price Variable Cost Sales mixHigh end t-shirt 25 8 1Budget t-shirt 10 2 10Moderate t-shirt 15 4 5Fixed costs are $2500 per month.What is the total number of break even units

Question

A business sells 3 products with the following information.Product Sales Price Variable Cost Sales mixHigh end t-shirt 25 8 1Budget t-shirt 10 2 10Moderate t-shirt 15 4 5Fixed costs are $2500 per month.What is the total number of break even units

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Solution

To calculate the total number of break-even units, we first need to calculate the weighted average contribution margin per unit.

  1. Calculate the contribution margin per unit for each product:

    • High end t-shirt: 2525 - 8 = $17
    • Budget t-shirt: 1010 - 2 = $8
    • Moderate t-shirt: 1515 - 4 = $11
  2. Calculate the weighted average contribution margin per unit:

    • High end t-shirt: 171=17 * 1 = 17
    • Budget t-shirt: 810=8 * 10 = 80
    • Moderate t-shirt: 115=11 * 5 = 55
    • Total contribution margin = 17+17 + 80 + 55=55 = 152
    • Weighted average contribution margin per unit = 152/(1+10+5)=152 / (1+10+5) = 152 / 16 = $9.5
  3. Calculate the total number of break-even units:

    • Break-even units = Fixed costs / Weighted average contribution margin per unit
    • Break-even units = 2500/2500 / 9.5 = approximately 263 units

So, the business needs to sell approximately 263 units to break even.

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