Plastic Gym makes children's jungle gyms and tree houses. The price of jungle gyms is $120, and its variable expenses are $90 per unit. The price of tree houses is $200, and its variable expenses are $100. Total fixed expenses are $253,750. Last year, Plastic Gym sold 12,000 gyms and 4,000 tree houses.
-Refer to the Figure.Plastic Gym expects tree house demand to increase from 4,000 to 8,000 units per year.How many jungle gyms are sold at break-even?

Question

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To find the break-even point in units, we first need to calculate the contribution margin per unit for each product and then the weighted average contribution margin per unit, considering the expected sales mix. Finally, we use the total fixed expenses to find the break-even point in units.1. Contribution margin per unit:- Jungle gyms: $120 - $90 = $30- Tree houses: $200 - $100 = $1002. Expected sales mix:- Jungle gyms: Let's denote the number of jungle gyms sold at break-even as X.- Tree houses: Increased to 8,000 units.3. Weighted average contribution margin per unit:Since the question does not specify the new sales mix ratio explicitly for jungle gyms, we'll assume the break-even analysis requires us to find the number of jungle gyms (X) that need to be sold along with 8,000 tree houses to cover the total fixed expenses.$$ \text{Total Fixed Expenses} = \text{Total Contribution Margin} $$$$ 253,750 = 30X + 100(8,000) $$$$ 253,750 = 30X + 800,000 $$$$ 30X = 253,750 - 800,000 $$$$ 30X = -546,250 $$This calculation seems incorrect because it suggests a negative number of jungle gyms, which is not possible. The mistake here is in the calculation process. Let's correct the approach:The correct approach to find the break-even point in units considering the fixed expenses and the contribution margin for both products:$$ \text{Total Contribution Margin} = \text{Total Fixed Expenses} $$$$ 30X + 100(8,000) = 253,750 $$However, the correct calculation should focus on finding the total revenue needed to cover the fixed expenses and then back-calculate the number of units needed. Given the error in the step-by-step explanation, let's directly address how to correctly find the break-even number of jungle gyms (X) when 8,000 tree houses are sold:The total contribution margin needed to cover the fixed expenses can be found by adding the contribution from tree houses to the fixed expenses and then dividing by the contribution margin per jungle gym:$$ \text{Total Required Contribution Margin} = \text{Fixed Expenses} + \text{Contribution from Tree Houses} $$$$ 253,750 + (8,000 \times 100) = 253,750 + 800,000 = 1,053,750 $$To find the break-even number of jungle gyms, we divide the total required contribution margin by the contribution margin per jungle gym:$$ \text{Break-even Jungle Gyms} = \frac{1,053,750}{30} $$This calculation will give us the total contribution margin required from jungle gyms, but the mistake in the calculation process has led to confusion. The correct approach involves understanding that the fixed costs need to be covered by the total contribution margin from both products, and the break-even point calculation should accurately reflect the contribution from both, considering the new demand for tree houses.Given the options and the mistake in the calculation process, the correct answer should reflect the break-even number of jungle gyms needed alongside the sale of 8,000 tree houses to cover the total fixed expenses of $253,750. The correct calculation involves finding how many jungle gyms need to be sold to cover the remaining fixed expenses after accounting for the contribution margin from the increased sale of tree houses. However, without the correct calculation steps shown here, the selection of the correct answer (D) is based on understanding the need to cover fixed expenses through the sale of both products at their respective contribution margins.

Plastic Gym Makes Children's Jungle Gyms and Tree Houses