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?
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.
To find the break-even level of monthly output, we need to determine the point at which the total revenue is equal to the total cost. The break-even point is where the firm neither makes a profit nor incurs a loss.
Let's denote the monthly output as x.
(i) To find the break-even level of monthly output, we can use the formula:
Total Revenue = Total Cost
The total revenue is given by the price per component multiplied by the number of units sold:
Total Revenue = Price per component * Monthly output
Total Revenue = $44 * x
The total cost consists of the fixed costs and the variable costs:
Total Cost = Fixed Costs + Variable Costs
The fixed costs are $40,000 per month, which remains constant regardless of the number of units sold.
The variable costs are $24 per component, so the total variable cost can be calculated as the variable cost per component multiplied by the number of units sold:
Variable Costs = Variable Cost per component * Monthly output
Variable Costs = $24 * x
Now, we can set up the equation for the break-even point:
Total Revenue = Total Cost
$44 * x = $40,000 + $24 * x
To find x, we need to isolate it on one side of the equation. Subtracting $24 * x from both sides:
$44 * x - $24 * x = $40,000
$20 * x = $40,000
Dividing both sides by $20:
x = $40,000 / $20
x = 2000
So, the break-even level of monthly output is 2000 units.
(ii) To find the monthly output at which the firm would make a profit of $10,000 per month, we need to consider the profit formula:
Profit = Total Revenue - Total Cost
We want the profit to be $10,000 per month, so the equation becomes:
$10,000 = $44 * x - ($40,000 + $24 * x)
Now, rearrange the equation to isolate x:
$44 * x - $24 * x = $40,000 + $10,000
$20 * x = $50,000
Divide both sides by $20:
x = $50,000 / $20
x = 2500
Therefore, the firm would need to produce 2500 components per month to make a profit of $10,000 per month.