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Give a real-world example of where a business would have a need to find a break-even or equilibrium point.

Consider a business that sells widgets around the country.  Say the widgets way between 1 and 4 lbs and therefore cost between 4 and 8 dollars to ship with the USPS.  The business needs to set a fixed standard shipping charge which will cover the expenses of  postage. Based on the ratio of different size widgets sold an equillibrium/break even point can be calculated.

Example for 100 widgets sold

• 50 were <2lbs ($4 to ship),
• 25 were 2 to <3 lbs ($6 to ship)
• 25 were 3 to 4 lbs ($8 to ship)

Equation for break even  point

x= ((50 x 4) + (25 x 6) + (25 x 8))/100

Here is a bus company which opreates a volume of kilometres.

The cost per kilometer is around 30 units on account of  fuel tyre and depreciation etc  which are direct cost (depending on kilometres).

There is a fixed over head cost on account of personnel, rent and cost of money , which works  out to 60000 per bus per month.

The average earning per kilometre is 40. The manager has to decide the break even operation by each of his bus.

Let k be the utilisation in kilometre operated by a bus in a month .

Then earning of the bus = k* earning per  klimetre =40 k

Cost of operation = Direct kilometer related cost+Fixed monthly cost=30k+60000.

In order to get profit , total earning > total cost.

40 k > 30k+60000. If we solve we get break even kilometrage.

40k-30k>60000

10k > 60000

Therefore k>6000. That implies 6000 kms is the break even kilometrage for a bus. If the manager operates less than 6000 kms per bus in a month he will be in loss and he will break even at the break even kms ,6000 kms with  no loss no profit. He will be in profits if he operates more than break even kilometrage.