Toucan Ltd sells three products and incurs $36,000 per period in fixed costs. The three products have the following characteristics: $\begin{array}{llcc}
\underline{\text { Product }} & \underline{\text { Price} } & \underline{\text {Variable Cost } } &\underline{\text { Sales Mix }}\
\text { P }&\$40& \$20&3 \text { units }\
\text { Q }&20& 10&9\text { units }\
\text { R }&49& 24&12 \text { units }\
\end{array}$
How many units of Product P will be sold at the breakeven point?

Question

Toucan Ltd sells three products and incurs $36,000 per period in fixed costs. The three products have the following characteristics: $\begin{array}{llcc}
\underline{\text { Product }} & \underline{\text { Price} } & \underline{\text {Variable Cost } }  &\underline{\text { Sales Mix }}\
 \text { P }&\$40& \$20&3 \text { units }\
 \text { Q }&20& 10&9\text { units }\
 \text { R }&49& 24&12 \text { units }\
\end{array}$
 How many units of Product P will be sold at the breakeven point?

Quizplus · Accepted Answer

The breakeven point is where total revenue equals total costs. Total costs are fixed costs plus variable costs. Variable costs are the sum of the variable costs per unit multiplied by the number of units sold. Total revenue is the sum of the prices per unit multiplied by the number of units sold.At the breakeven point, total revenue equals total costs:$$P 	imes Q_P + Q 	imes Q_Q + R 	imes Q_R = FC + VC_P 	imes Q_P + VC_Q 	imes Q_Q + VC_R 	imes Q_R$$Substituting the given values, we get:$$40 	imes Q_P + 20 	imes 9 + 49 	imes 12 = 36,000 + 20 	imes Q_P + 10 	imes 9 + 24 	imes 12$$Simplifying, we get:$$20 	imes Q_P = 36,000 - 20 	imes 9 - 10 	imes 9 - 24 	imes 12$$$$20 	imes Q_P = 36,000 - 180 - 90 - 288$$$$20 	imes Q_P = 35,532$$$$Q_P = 1,776.6$$Therefore, the number of units of Product P that will be sold at the breakeven point is 1,776.6.

Toucan Ltd Sells Three Products and Incurs $36,000 Per Period