Single: What are Sales

Suppose your firm has a break-even point in sales on one of your product lines of $700000. Variable expenses are 70% of sales. If you lost $30,000 on the product line last year, sales must have been …


This one is just a little algebra. We make an assumption that the cost functions are linear, $C= F + \alpha q$. Since we know $\alpha =.7$ from the set up of the problem but we have to sort out the fixed cost, F. Here is where the information on the break even point is important. It allows us to identify the fixed cost. When know that when the q is 70000 that the revenue is equal to the cost, $q=F+\alpha q$. Given that we can solve for F.

\begin{equation} F +(0.7 )(700000) =700000 \end{equation}
\begin{equation} F=(0.3) (700000)= 210000 \end{equation}

Now we have the full cost function, $C=210000+.7 q$

To sort out the sales you just take the the difference between revenue and costs and set it equal to your known loss, 30000, and solve for q.

\begin{equation} -30000=q - 210000 -.7 q \end{equation}

So, sales were 600000, which is less than the break-even point and consistent with the $30000 loss.

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