It has to sell 100 mugs.
Remember that profit (P), Revenue (R), and cost (C) are related by the following formula:
[tex]P=R-C[/tex]
The term break- even point occurs when the Revenue is equal to the Cost, making the profit to be equal zero. In other words:
[tex]0=R-C \\ \\ R=C[/tex]
A manufacturer produces mugs at a cost of $2 daily. The company also has daily costs of $500. So each day the cost for the company is:
[tex]C=500[/tex]
So the number of mugs the company produces every day is:
[tex]No. \ mugs=\frac{\$500}{\$2}=250[/tex]
We also know that the company sells the mugs for $5, so the revenue is:
[tex]R=5x \\ \\ \\ x:\text{Number of mugs it has to sell tocover all daily costs}[/tex]
Then by equating equations:
[tex]5x=500 \\ \\ Isolating \ x: \\ \\ x=\frac{500}{5} \\ \\ x=100[/tex]
So the company has to sell 100 out of 250 mugs it produces daily in order to cover all daily costs.
