Question

Rose Corporation sells backpacks. Variable costs for this product are $30 per unit, and the sales price per unit is $50 per unit. Total fixed costs amount to $100,000. How many backpacks does Rose need to sell to achieve a desired profit of $60,000?

Answer 1

To calculate total revenue, multiply the sales price per unit by the number of units sold. Determine total cost by adding the total variable cost and fixed cost. Find the profit-maximizing quantity by identifying where marginal revenue equals marginal cost, which is 2 units.

Step-by-step explanation:

To calculate the total revenue, multiply the sales price per unit ($72) by the number of units sold. The total cost is the sum of the total variable cost and the fixed cost. Marginal revenue is the change in total revenue when one additional unit is sold. Marginal cost is the change in total cost when one additional unit is produced. To find the profit-maximizing quantity, examine the point where marginal revenue equals marginal cost.

Here is a table summarizing the calculations:
Output Level
Total Revenue
Marginal Revenue
Total Cost
Marginal Cost

1
$72
$72
$164
$100

2
$144
$72
$189
$25

3
$216
$72
$223
$34


4
$288
$72
$275
$52


5
$360
$72
$350
$75

In the total revenue and total cost curve diagram, the total revenue curve is upward-sloping and the total cost curve is upward-sloping, but at a steeper slope. In the marginal revenue and marginal cost curve diagram, both curves are downward-sloping, with the marginal revenue curve crossing the marginal cost curve at the output level of 2 units. Therefore, the profit maximizing quantity is 2 units.

Answer 2

8,000

Step-by-step explanation:

Profit = Total revenue - Total cost

Total revenue = price × quantity sold

Total cost = Fixed cost + variable cost

Variable cost = Cost x quantity sold

Profit = $60,000

Total revenue = $50 × quantity sold (Q) = 50Q

Variable cost = $30 x quantity sold (Q) = $30Q

Fixed cost = $100,000

Total cost = $100,000 + $30Q

$60,000 = $50Q - ($100,000 + $30Q)

$60,000 = $20Q - $100,000

$160,000 = $20Q

Q = 8,000

I hope my answer helps you