Question

Alpha Company sells their product for $ 1 each. The variable costs are $ 7 per unit and the fixed costs are $ 30,000 per year. How much should we sell the unit to: 1- Reach the break-even point 2- Achieve a net profit of $ 21,000 3- Achieve a net profit equal to $ 21,000.

Answer 1

we have that

Part 1

Remember that breakpoint is when the revenue (R) is equal to the cost (C)

so

C=7x+30,000

R=10x

equate both equations

10x=7x+30,000

solve for x

10x-7x=30,000

3x=30,000

x=10,000 units

the answer Part 1 is 10,000 units

Part 2

net profit of $ 21,000

so

R-C=21,000

10x-(7x+30,000)=21,000

10x-7x-30,000=21,000

3x=21,000+30,000

3x=51,000

x=17,000 units

Part 3

net profit equal to $ 60,000

so

R-C=60,000

10x-(7x+30,000)=60,000

10x-7x-30,000=60,000

3x=60,000+30,000

3x=90,000

x=30,000 units