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?

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BlackTom AI · Accepted Answer

We start by restating the problem details and the options to keep everything clear. 
Question: A startup called RoboBar makes two types of custom protein bars: Chocolate Power and Peanut Blast. Annual demand is 10,000 Chocolate Power bars at 6 minutes of processing each, produced in lots of 500 units with 0.5 hours of setup per lot. Peanut Blast has annual demand 5,000 units at 12 minutes per unit, 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 a 10% capacity cushion is required. How many mixing machines are needed?
Answer options: 4, 3, 5, 2

Step 1: Convert processing time into hours and account for setup times for Chocolate Power.
- Chocolate Power demand = 10,000 units. Processing time = 6 minutes per unit → 10,000 × 6 minutes = 60,000 minutes = 1,000 hours.
- Lot size = 500 units, so number of lots = 10,000 / 500 = 20 lots. Setup time per lot = 0.5 hours, so total setup time = 20 × 0.5 = 10 hours.
- Total annual time for Chocolate Power = processing hours + setup hours = 1,000 + 10 = 1,010 hours.

Step 2: Convert processing time into hours and account for setup times for Peanut Blast.
- Peanut Blast demand = 5,000 units. Processing time = 12 minutes per unit → 5,000 × 12 minutes = 60,000 minutes = 1,000 hours.
- Lot size = 250 units, so number of lots = 5,000 / 250 = 20 lots. Setup time per lot = 1 hour, so total setup time = 20 × 1 = 20 hours.
- Total annual time for Peanut Blast = processing hours + setup hours = 1,000 + 20 = 1,020 hours.

Step 3: Combine totals from both products to get the overall machine-hour requirement.
- Combined processing and setup time = 1,010 hours + 1,020 hours = 2,030 hours per year.

Step 4: Apply the 10% capacity cushion to the machine’s available hours.
- Each machine has 1,000 hours/year, but we reserve 10% for cushion, so usable hours per machine = 1,000 × (1 − 0.10) = 900 hours/year.

Step 5: Compute the number of machines needed and interpret the result.
- Required machines = total hours needed / usable hours per machine = 2,030 / 900 ≈ 2.26.
- Since you can’t operate a fraction of a machine, you round up to the next whole machine, which means 3 machines are required.

Step 6: Evaluate the given options against the calculation.
- Option 4 would overestimate the capacity greatly relative to the computed need.
- Option 3 matches the rounded-up result from the calculation, reflecting a practical number of machines given the cushion and workload.
- Option 5 is unnecessarily high for the computed requirement and would imply unused capacity.
- Option 2 would be insufficient because 2 machines would provide only about 1,800 usable hours (2 × 900), which is well below the required 2,030 hours.

Overall, the sensible interpretation of the data leads to a rounded-up machine count that aligns with the option corresponding to 3.

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