Approximately 2,186,734 pounds of cacao beans are needed for the production of Hershey bars for the next 30 days based on the given information and calculations.
Let's break this down step by step to find the pounds of cacao beans required for the production of Hershey bars for the next 30 days.
Given Information:
1. Manufacturing Operation Hours: 8760 hours per year
2. Cacao Beans to Chocolate Ratio: 2 pounds of cacao beans produce 1 pound of chocolate
3. Wastage during Production: 2% of beans are wasted
4. Production Schedule for Next 30 Days:
- 12,000,000 plain Hershey bars
- Each bar weighs 1.75 ounces
- Bars contain 80% chocolate from beans and 20% from other ingredients
5. Losses within Chocolate Bar Manufacturing Processes: 2%
Calculation Steps:
Step 1: Calculate Total Chocolate Needed for 12,000,000 Bars
1. Convert bar weight from ounces to pounds:
- 1.75 ounces per bar × (1 pound / 16 ounces) = 0.109375 pounds per bar
2. Calculate total chocolate needed for 12,000,000 bars:
- Total chocolate = Total bars × Weight of chocolate per bar × Percentage of chocolate from beans
- Total chocolate = 12,000,000 bars × 0.109375 pounds per bar × 80%
- Total chocolate = 12,000,000 × 0.109375 × 0.80 = 1,050,000 pounds
Step 2: Account for Cacao Beans Required
1. Since 2 pounds of cacao beans produce 1 pound of chocolate:
- Cacao beans needed = Total chocolate needed × Cacao beans to chocolate ratio
- Cacao beans needed = 1,050,000 pounds × 2
- Cacao beans needed = 2,100,000 pounds
Step 3: Adjust for Wastage
1. Considering 2% wastage during production:
- Wasted beans = Cacao beans needed × Wastage percentage
- Wasted beans = 2,100,000 pounds × 0.02 = 42,000 pounds
2. Total beans required, accounting for wastage:
- Total beans required = Cacao beans needed + Wasted beans
- Total beans required = 2,100,000 pounds + 42,000 pounds = 2,142,000 pounds
Step 4: Account for Losses in Manufacturing Processes
1. Considering losses within the chocolate bar manufacturing processes (2%):
- Final beans needed = Total beans required / (1 - Loss percentage)
- Final beans needed = 2,142,000 pounds / (1 - 0.02)
- Final beans needed = 2,142,000 pounds / 0.98 ≈ 2,186,734 pounds