answer:To calculate the utilization rate for each stage, we need to compare the actual production rate to the maximum possible production rate. For Stage A, the maximum possible production rate is 80 units per minute, but due to the bottleneck in Stage B, the actual production rate for Stage A is also limited to 40 units per minute (since Stage A cannot produce more than what Stage B can process). The utilization rate for Stage A is therefore (40/80) x 100% = 50%. For Stage B, the maximum possible production rate is 40 units per minute, and the actual production rate is also 40 units per minute (since it is the bottleneck). The utilization rate for Stage B is therefore (40/40) x 100% = 100%. So, the utilization rates are 50% for Stage A and 100% for Stage B.

answer:An overall utilization rate of 50% in Stage A indicates that half of the capacity of Stage A is not being utilized. This means that the machines in Stage A are idle for half of the time they could be producing, resulting in underutilization of resources and potentially wasted investment in equipment and personnel. This low utilization rate is a result of the bottleneck in Stage B, which is limiting the entire production line. To address this issue, there are several options to consider: 1. **Increase the capacity of Stage B**: By adding more machines or upgrading the existing ones, the capacity of Stage B can be increased, allowing it to process more units per minute and thereby increasing the overall production rate. This would also increase the utilization rate of Stage A. 2. **Improve the efficiency of Stage B**: Identifying and addressing inefficiencies in Stage B, such as process changes or maintenance improvements, could also increase its capacity without requiring additional machines. 3. **Rebalance the line**: If possible, rebalancing the line by moving some machines from Stage A to Stage B could help to better match the capacities of the two stages. 4. **Run Stage A in batches**: If it's not feasible to increase the capacity of Stage B, an alternative could be to run Stage A in batches, accumulating inventory between stages, and then feeding it into Stage B as needed. However, this approach would require additional storage space and inventory management. 5. **Consider outsourcing or reconfiguring Stage B**: If the above options are not feasible, it might be worth considering outsourcing Stage B or reconfiguring the production line to eliminate the bottleneck.

answer:To solve this problem, we need to determine the value of x, which represents the total number of pairs of shoes Sue owns. Let's break down the information given: Number of identical black pairs of shoes: 6 Number of identical brown pairs of shoes: 3 Number of identical gray pairs of shoes: 2 We can set up the equation as follows: Number of identical black pairs of shoes + Number of identical brown pairs of shoes + Number of identical gray pairs of shoes = Total number of pairs of shoes 6 + 3 + 2 = x Let's simplify and solve for x: 11 = x Therefore, the value of the unknown variable x is 11. Sue owns 11 pairs of shoes. The answer is: 11

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