Party trays, which cost $14.00 to make not including labor, are sold for $35.00. If two people work 8-hour shifts making the trays at $7.00 per hour, how many trays must be sold to cover all costs including labor?
The Correct Answer and Explanation is:
Let’s break down the problem step-by-step:
Given:
- Cost to make one tray (excluding labor) = \$14.00
- Selling price per tray = \$35.00
- Two people work 8-hour shifts making trays
- Labor cost per hour per person = \$7.00
- Need to find: How many trays must be sold to cover all costs, including labor?
Step 1: Calculate total labor cost
- Number of workers = 2
- Hours worked per worker = 8
- Hourly wage per worker = \$7.00
Total labor cost = Number of workers × Hours worked × Hourly wage
= 2 × 8 × \$7.00
= 16 × \$7.00
= \$112.00
Step 2: Calculate total cost for making trays
Let the number of trays made be x.
- Material cost per tray = \$14.00
- Labor cost total = \$112.00 (fixed for this batch)
- Total cost = (Material cost per tray × number of trays) + labor cost
= 14x + 112
Step 3: Calculate revenue from selling trays
- Selling price per tray = \$35.00
- Revenue from selling x trays = 35x
Step 4: Set revenue equal to total cost to find break-even number of trays
To cover all costs, revenue must be at least equal to total cost:
$$
35x = 14x + 112
$$
Subtract 14x from both sides:
$$
35x – 14x = 112
$$
$$
21x = 112
$$
Divide both sides by 21:
$$
x = \frac{112}{21} \approx 5.33
$$
Step 5: Interpret the result
Since you can’t sell a fraction of a tray, you must sell at least 6 trays to cover all costs including labor.
Final Answer:
6 trays must be sold to cover all costs including labor.
Explanation:
This problem involves understanding fixed and variable costs and how they contribute to the break-even point. The material cost per tray (\$14) is a variable cost because it changes depending on the number of trays made. The labor cost (\$112) is a fixed cost for the shift because it doesn’t depend on the number of trays — the workers are paid for 8 hours regardless.
To break even, total revenue (selling price × number of trays) must equal total costs (material + labor). By setting these equal, we solve for the minimum number of trays to sell to avoid losing money.
It’s important to note that even though the cost per tray (without labor) is \$14, the labor adds a significant fixed expense that spreads out over the trays. Selling only 5 trays yields revenue of 5 × \$35 = \$175 but costs are 5 × \$14 + \$112 = \$182, resulting in a loss. Selling 6 trays yields revenue of \$210 and costs of \$196, so the business starts to make a profit.
Thus, understanding how fixed costs like labor impact overall profitability is essential in pricing and production decisions in business.