Question

9. The owner of shop is contemplating to add a new product, which will require additional monthly payment of $ 20,000. Variable costs would be $ 5.00 per new product, and its selling price is planned to be $ 8.00 each. a. How many new products must be sold in order to break-even? b. What would the profit (loss) be if 2,000 units were sold in a month? c. How many units must be sold to realize a profit of $ 5,000?

Answer 1

a. To break-even, the total revenue must equal the total cost. Let x be the number of new products that must be sold in order to break-even. Then, the equation is:

Total revenue = Total cost

8x = 20000 + 5x

3x = 20000

x = 20000/3

x ≈ 6666.67

Therefore, the shop owner must sell at least 6,667 new products in a month to break-even.

b. If 2,000 units are sold in a month, the total revenue is:

Total revenue = Selling price x Quantity

Total revenue = 8 x 2000

Total revenue = $16,000

The total cost is the sum of the fixed cost and the variable cost:

Total cost = Fixed cost + Variable cost

Total cost = 20000 + 5 x 2000

Total cost = $30,000

Therefore, the profit (loss) would be:

Profit (loss) = Total revenue - Total cost

Profit (loss) = 16,000 - 30,000

Profit (loss) = -$14,000 (loss)

c. To realize a profit of $5,000, the equation for total profit is:

Total profit = Total revenue - Total cost

Total profit = (Selling price x Quantity) - (Fixed cost + Variable cost)

Total profit = (8x) - (20000 + 5x)

Setting the equation equal to the desired profit and solving for x:

5000 = (8x) - (20000 + 5x)

5000 = 3x - 20000

25000 = 3x

x ≈ 8333.33

Therefore, the shop owner must sell at least 8,334 new products in a month to realize a profit of $5,000.

Step-by-step explanation: