Question

E = 7.40q + 56,000. Its products will be sold to retailers at a wholesale price of R = 129 each. How many items must be sold to reach the breakeven point? (hint: E = R)

a) 7,568 items
b) 10,000 items
c) 5,000 items
d) 12,000 items

Answer 1

The breakeven point is reached when 461 items are sold, as at this point revenue from sales matches the total expenses. Solving the equation 129q = 7.40q + 56,000, where q is the number of items, gives us the solution.

Step-by-step explanation:

To find the breakeven point, we need to determine the number of items that must be sold so that the revenue equals the expenses. According to the given equation E = 7.40q + 56,000, where E represents the total expenses and q is the quantity of items produced and sold, the firm's expenses increase by $7.40 for each additional item. The revenue R for each item sold is $129.

To find the breakeven point, we set the revenue equal to the expenses (E = R). Therefore, 129q = 7.40q + 56,000. Solving for q, we subtract 7.40q from both sides, which gives us 121.6q = 56,000. Then, divide both sides by 121.6 to find q, which yields q = 460.53. Since we cannot sell a fraction of an item, we round up to the nearest whole number, resulting in 461 items needed to be sold to reach the breakeven point.