ABC company wants to sell enough products to earn a profit of $40,000, if unit sales are $10 and variable costs $8 , fixed cost $80,000 how many units must be sold to earn a profit of $40,000. Any assistance would be greatly appreciated!

Best Regards,
Vernessa

 

Hi Vernessa,

The amount of profit you earn depends on the number of units sold so let x be the number of items sold. Since a unit sells for $10 your income I(x) is given by

I(x) = $10 x

You have two kinds of costs, a fixed cost and a variable cost. The fixed cost is $40,000. This is the cost for thinks like heating, lighting, building rental, etc. Things that don't depend on the number of unite you produce. Then you have a variable cost of $8 per unit. This is what it cost you produce an item, things like employee wages, materials, etc. Thus to produce x units you cost C(x) is given by

C(x) = $40,000 + $8 x

The profit you make after producing x units P(x) is your income minus your costs thus

P(x) = I(x) - C(x)

You want a profit of P(x) = $40,00. Solve for x.

Penny