Question
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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?

Ask by Goodwin Ryan. in the United States
Dec 03,2024

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Tutor-Verified Answer

Answer

Se deben vender 4 bandejas para cubrir todos los costos, incluyendo el costo laboral.

Solution

Para resolver este problema, primero calculamos el costo total de fabricar una bandeja, que incluye el costo de los materiales y el costo laboral. Luego, calculamos cuántas bandejas deben venderse para cubrir todos los costos, incluyendo el costo laboral. 1. **Costo de materiales por bandeja:** \( \$ 14.00 \) 2. **Costo laboral por hora:** \( \$ 7.00 \) 3. **Tiempo de trabajo por persona:** 8 horas 4. **Número de personas trabajando:** 2 personas 5. **Costo laboral total por bandeja:** \( 2 \text{ personas} \times 8 \text{ horas} \times \$ 7.00/\text{hora} = \$ 112.00 \) 6. **Costo total por bandeja (materiales + laboral):** \( \$ 14.00 + \$ 112.00 = \$ 126.00 \) 7. **Precio de venta por bandeja:** \( \$ 35.00 \) 8. **Número de bandejas que deben venderse para cubrir todos los costos:** \( \frac{\text{Costo total por bandeja}}{\text{Precio de venta por bandeja}} = \frac{\$ 126.00}{\$ 35.00} \approx 3.6 \) Debido a que no se puede vender una parte de una bandeja, se deben vender 4 bandejas para cubrir todos los costos, incluyendo el costo laboral.

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First, let's calculate the labor costs. With two people working 8-hour shifts at \( \$ 7.00 \) per hour, the total labor cost for one shift (16 hours) is \( 2 \times 8 \times 7 = \$ 112.00 \). Now, adding the cost to make one party tray, which is \( \$ 14.00 \), to the labor cost gives a total cost of \( \$ 112.00 + \$ 14.00 = \$ 126.00 \) for one tray. To find the number of trays that need to be sold to cover costs, we first determine the profit per tray sold. Selling each tray for \( \$ 35.00 \), the profit on one tray is \( 35.00 - 14.00 = \$ 21.00 \). Now, to cover \( \$ 126.00 \) in costs, you need to sell: \[ \frac{126}{21} = 6 \text{ trays}. \] So, you must sell 6 trays to cover all costs including labor!

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