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Pawsome Playthings are a business that makes dog toys. The business has provided the following information:Product Sales Price Variable Cost Sales mixSqueaky Plush Toys 15 10.50 15Tug Rope Toys 10 5.00 10Treat-Dispensing Toys 30 12.00 7Fixed costs are $6,700.How many items in total need to be sold to break even? Please answer in whole units

Question

Pawsome Playthings are a business that makes dog toys. The business has provided the following information:Product Sales Price Variable Cost Sales mixSqueaky Plush Toys 15 10.50 15Tug Rope Toys 10 5.00 10Treat-Dispensing Toys 30 12.00 7Fixed costs are $6,700.How many items in total need to be sold to break even? Please answer in whole units

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Solution

To calculate the break-even point, we first need to calculate the weighted average contribution margin per unit for each product. The contribution margin is the sales price minus the variable cost. The weighted average takes into account the sales mix.

  1. Squeaky Plush Toys: Contribution Margin = Sales Price - Variable Cost = 1515 - 10.50 = 4.50WeightedContributionMargin=ContributionMarginSalesMix=4.50 Weighted Contribution Margin = Contribution Margin * Sales Mix = 4.50 * 15 = $67.50

  2. Tug Rope Toys: Contribution Margin = Sales Price - Variable Cost = 1010 - 5 = 5WeightedContributionMargin=ContributionMarginSalesMix=5 Weighted Contribution Margin = Contribution Margin * Sales Mix = 5 * 10 = $50

  3. Treat-Dispensing Toys: Contribution Margin = Sales Price - Variable Cost = 3030 - 12 = 18WeightedContributionMargin=ContributionMarginSalesMix=18 Weighted Contribution Margin = Contribution Margin * Sales Mix = 18 * 7 = $126

Next, we add up the weighted contribution margins to get the total weighted average contribution margin per unit:

Total Weighted Average Contribution Margin = 67.50+67.50 + 50 + 126=126 = 243.50

Then, we divide the total fixed costs by the total weighted average contribution margin to get the break-even point in units:

Break-Even Point in Units = Total Fixed Costs / Total Weighted Average Contribution Margin = 6,700/6,700 / 243.50 = 27.5 units

Since we can't sell half a unit, we round up to the nearest whole unit. So, Pawsome Playthings needs to sell 28 units in total to break even.

This problem has been solved

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