A firm that produces car components has a fixed costs of $ 40,000 per month and a variable cost of $ 24 per component.it sells its product at a price of $ 44 per component,regardless of the number of units sold. (i)find the break-even level of monthly output. (ii) at what monthly output would the firm make a profit of $10000 per month?

2 answers

2000
(i) The break-even point occurs when the revenue equals the total cost. Let's denote the monthly output by Q. Then we can write:

Revenue = Price × Quantity
Cost = Fixed cost + Variable cost × Quantity

Setting these two expressions equal to each other, we get:

Price × Quantity = Fixed cost + Variable cost × Quantity

Simplifying, we get:

(Price - Variable cost) × Quantity = Fixed cost

Substituting the given values, we get:

(44 - 24) × Q = 40,000

Solving for Q, we get:

Q = 2,000

Therefore, the break-even level of monthly output is 2,000 components.

(ii) Let's denote the monthly output that results in a profit of $10,000 by Q'. We can use a similar approach as in part (i) and write:

Price × Quantity - (Fixed cost + Variable cost × Quantity) = Profit

Substituting the given values and the profit of $10,000, we get:

44 × Q' - (40,000 + 24 × Q') = 10,000

Solving for Q', we get:

Q' = 3,000

Therefore, the monthly output that results in a profit of $10,000 is 3,000 components.