Question

Alpha Company sells their product for $ 10 each. The variable costs are $ 7 per unit and the fixed costs are $ 30,000 per year. What is the number of units they need to sell to: 1- Reaching the breakeven point 2- Achieving a net profit of $ 21,000 3- Achieving a net profit equal to $ 60.000

Answer 1

Let x be the number of units produce and sold (in here we are assuming that all the units the company make are sold).

Since the company sells the product for $10 the profit is given by:

`10x`

Now, since the variable cost is $7 and the fixed cost is 30.000 then the total cost is given by:

`7x-3000`

Finally the total revenue is given by the profit minus the cost, then we have the equation:

`y=10x-(7x+30000)`

1.

The break even point is reach when the revenue is zero, then we have:

`\begin{gathered} 10x-(7x+30000)=0 \\ 10x-7x-30000=0 \\ 3x=30000 \\ x=(30000)/(3) \\ x=10000 \end{gathered}`

Therefore they need to sell 10,000 units to break even.

2.

To ahieve a net profit of 21,000 we equate or expression to this amount and solve for x: