Final answer:
To achieve the optimal number of buckets, the workers should be assigned to produce both round and square pieces. With 42 workers, each capable of producing 120 round pieces or 80 square pieces per hour will result in the production of 2,520 buckets per hour.
Step-by-step explanation:
To achieve the optimal number of buckets, the workers should be assigned to produce both round and square pieces. Let's break it down step-by-step:
- Each worker can produce 120 round pieces per hour or 80 square pieces per hour.
- To make a bucket, we need 2 round pieces and 1 square piece.
- Let's assume we assign all workers to produce round pieces only. With 42 workers, they can produce a total of 120 x 42 = 5,040 round pieces per hour.
- Now, let's calculate the number of buckets we can make using these round pieces. Since we need 2 round pieces per bucket, we can make a maximum of 5,040 / 2 = 2,520 buckets per hour.
- Similarly, if we assign all workers to produce square pieces only, they can produce 80 x 42 = 3,360 square pieces per hour. Based on the requirement of 1 square piece per bucket, we can make a maximum of 3,360 / 1 = 3,360 buckets per hour.
- However, if we assign each worker to produce both round and square pieces, each worker can produce 120 round pieces and 80 square pieces per hour. This means that with 42 workers, we can make 120 x 42 = 5,040 round pieces and 80 x 42 = 3,360 square pieces per hour.
- Using these quantities, we can calculate the number of buckets we can make. With 5,040 round pieces and 3,360 square pieces, we can make a maximum of min(5,040 / 2, 3,360 / 1) = 2,520 buckets per hour.
Therefore, by assigning each worker to produce both round and square pieces, we can achieve the optimal number of 2,520 buckets per hour.