A startup called RoboBar makes two types of custom protein bars: Chocolate Power and Peanut Blast. The company estimates that the annual demand for Chocolate Power bars is 10,000 units, and each bar requires 6 minutes of processing on the mixing machine. Chocolate Power bars are produced in lots of 500 units, with each lot requiring 0.5 hours of setup. Peanut Blast bars have an annual demand of 5,000 units, and each bar requires 12 minutes of processing. Peanut Blast is produced in lots of 250 units, with 1 hour of setup per lot. Each mixing machine is available for 1,000 hours per year, and the company wants to maintain a 10% capacity cushion. How many mixing machines are required to meet the annual demand?

Question

BlackTom AI · Accepted Answer

We’re asked to determine how many mixing machines RoboBar needs to meet annual demand with a 10% capacity cushion. Here’s a step-by-step breakdown of the calculations and evaluation of each option.

First, compute the annual processing time required for each product:
- Chocolate Power: demand 10,000 units, 6 minutes per bar.
  - Processing time = 10,000 bars × 6 minutes = 60,000 minutes = 1,000 hours.
- Peanut Blast: demand 5,000 units, 12 minutes per bar.
  - Processing time = 5,000 bars × 12 minutes = 60,000 minutes = 1,000 hours.

Next, account for lot-based setup times:
- Chocolate Power: lots of 500 units ⇒ 10,000 / 500 = 20 lots. Setup per lot = 0.5 hours.
  - Total setup time = 20 × 0.5 = 10 hours.
- Peanut Blast: lots of 250 units ⇒ 5,000 / 250 = 20 lots. Setup per lot = 1 hour.
  - Total setup time = 20 × 1 = 20 hours.

Total annual hours on the mixing machine required:
- Chocolate Power total = 1,000 (processing) + 10 (setup) = 1,010 hours.
- Peanut Blast total = 1,000 (processing) + 20 (setup) = 1,020 hours.
- Combined total = 1,010 + 1,020 = 2,030 hours per year.

Now consider machine capacity with a 10% cushion:
- Each machine has 1,000 hours per year available, but with a 10% cushion, usable hours per machine = 1,000 × (1 − 0.10) = 900 hours/year.

Required number of machines = total hours required / usable hours per machine = 2,030 / 900 ≈ 2.26 machines.
Since we can’t have a fraction of a machine, we need to round up to the next whole machine, which is 3.

Evaluation of each option:
- Option 4: 4 machines would provide 4 × 900 = 3,600 usable hours, which is more than enough, but it overstates needs and would be more expensive than necessary.
- Option 3: 3 machines provide 3 × 900 = 2,700 usable hours, which comfortably covers the required 2,030 hours with the 10% cushion. This is the minimum that satisfies demand.
- Option 2: 2 machines provide 2 × 900 = 1,800 usable hours, which is insufficient to cover 2,030 hours of required work even before any additional buffers.
- Option 5: 5 machines would yield 4,500 usable hours, far exceeding needs and thus is unnecessarily large.

Therefore, the calculations show that 3 machines are needed to meet the annual demand while maintaining the required capacity cushion.

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View Explanation

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