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This is the required amount of operating income of $161,200 divided by the weighted average contribution margin of $6.20. The numerator of this calculation needs to be the total fixed costs plus the required amount of operating income. Furthermore, the resulting number of units will be the total number of units that will need to be sold of all products, not the number of unit sold required of Product No. 153.
This is a breakeven analysis when more than one product is sold combined with the requirement for a certain amount of operating income. 109 145 153 Estimated Sales Volume 30,000 75,000 45,000 Percentage of Total (150,000) 20% 50% 30% Selling price 10.00 15.00 20.00 Variable cost 5.50 8.00 14.00 Contribution margin 4.50 7.00 6.00 The weighted average contribution margin for the mix is: (.20 × 4.50) + (.50 × 7.00) + (.30 × 6.00) = $6.20 Required number of total units for a $161,200 operating profit with $961,000 in fixed costs: (961,000 + 161,200) / 6.20 = 181,000 total units of all products Product No.153 is 30% of that. So the number of units of No. 153 that need to be sold to generate the required amount of operating income is .30 × 181,000, or 54,300.
This is the total number of units that need to be sold, but this number includes all three products. The question asks for the number of units of Product No. 153 that would need to be sold.
This is the total fixed costs of $961,000 divided by the weighted average contribution margin of $6.20. This is the total number of units of all the products that would need to be sold in order to break even. This calculation does not include consideration for the requirement that operating income should be $161,200, plus the resulting number of units is the total number of units that need to be sold of all products, not the number of units needed for Product No. 153.