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:

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

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:

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