Question

Abc audio sells headphones and would like to earn after tax profit of $400 every week. each set of headphones costs $5 and is sold for $10. they also incur costs of $200 for rent and other fixed costs, and their tax rate is 20%. how many headphones must they sell per week to meet this goal?abc audio sells headphones and would like to earn after tax profit of $400 every week. each set of headphones costs $5 and is sold for $10. they also incur costs of $200 for rent and other fixed costs, and their tax rate is 20%. how many headphones must they sell per week to meet this goal?

Answer 1

Let us denote the number of headphones with h. If tax rate applies on the revenue of 10h, then the cost and the revenue can be calculated as: cost= 5h + 200revenue=10h - 0.2(10h) = 8h
8h - (5h + 200) = 4008h - 5h - 200 = 4003h = 600h = 200
So, in order to meet the goal of $400 we should sell 200 headphones.

Answer 2

Taxes are paid on net profits, so income applied to fixed and variable costs is not taxed. Since the fixed costs are $200 per week, and ABC audio clears $5 on each set of headphones, the fixed costs will be met once ABC has sold 40 sets. For each $10 of income for every additional set sold, ABC pays a 20% tax on the $5 cleared after variable costs are accounted for, leaving $4 profit. So, to make $400 profit for the week, ABC audio will need to sell an additonal 100 sets. Thus, accounting for fixed costs, variable costs, and taxes, ABC must sell 140 sets of headphones per week to generate $400 in profit.