Level of activity, where [color=#0000ff]sales proceeds equals with total costs[/color], is called as [color=#0000ff]critical point[/color]. It can be expressed either in currency or as a number of products. At critical point, margin profit and fixed costs also equal, so it can be solved also with formula[br][br] [math]\large \textcolor{blue}{\text{Critical point (€)}=\frac{\text{Fixed costs (€)}}{\text{Profit margin for a product}}}.[/math][br][br]With the formula[br] [math]\large \textcolor{blue}{\text{Critical point (€)}=\frac{\text{Fixed costs (€)}}{\text{Profit margin in \%}}\cdot 100}[/math][br][br]can be solved the sales in euros covering fixed costs. [br]

How many tickets should students have sold for not to make any loss?[br][br][u]Option 1:[br][/u][br]The ticket price includes also VAT, so the actual unit price is 13.64€[br]  [br]Unit margin profit for a customer is [math] 13.64€-4€=9.64€.[/math] If the profit margin ratio is known, then the unit profit margin can also be solved with it as follows: [br][br][math]\text{profin margin ratio}\cdot \text{unit price }=70.67\%\cdot 13.64€= 9.64€[/math][br][br]The fixed costs should be covered, so[br][br]   [math] \begin{eqnarray}[br]9.64€\cdot x&=&550€\\[br]x&=&\frac{550€}{9.64€}=57.1\end{eqnarray}[/math][br][br]Had they sold 57 tickets, they would have earned 549.48€. It is not enough. Thus, they should have sold 58 tickets.[br][br][u]Option 2:[/u][br][br]This can be solved also with an equation, where sales proceeds and total costs equal:[br][br]   [math]\begin{eqnarray}[br]13.64€\cdot x&=& 4x+550\\[br]9.64€\cdot x&=&550€\\[br]x&=&57.1[br]\end{eqnarray}[br][/math][br][br]