题目信息
| Components | Number of components: | ||
| Monday | Tuesday | Wednesday | |
| A | 3 | 6 | 3 |
| B | 6 | 3 | 4 |
| C | 4 | 7 | 4 |
A factory assembles Product X from three components, A, B, and C. One of each component is needed for each Product X and all three components must be available when assembly of each Product X starts. It takes two days to assemble one Product X. Assembly of each Product X starts at the beginning of one day and is finished at the end of the next day. The factory can work on at most five Product Xs at once. If components are available each day as shown in the table above, what is the largest number of Product Xs that can be assembled during the three days covered by the table?
A:3
B:5
C:6
D:9
E:10
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正确答案：
B:5
Arithmetic Applied problems
We will determine the largest number of Product Xs that can be assembled during all three days by considering separately the largest number that can be assembled if 0, 1, 2, or 3 Product Xs begin assembly on Monday.
0 Product Xs begin assembly on Monday: In this case, at most three Product Xs can begin assembly on Tuesday (because only three units of Component A are available on Wednesday), and hence at most 0 + 3 = 3 Product Xs could be assembled during the three days.
1 Product X begins assembly on Monday: In this case, at most three Product Xs can begin assembly on Tuesday (because only three units of Component A are available on Wednesday), and hence at most 1 + 3 = 4 Product Xs could be assembled during the three days.
2 Product Xs begin assembly on Monday: In this case, at most three Product Xs can begin assembly on Tuesday (because only three units of Component A are available on Wednesday), and hence at most 2 + 3 = 5 Product Xs could be assembled during the three days.
3 Product Xs begin assembly on Monday: In this case, at most two Product Xs can begin assembly on Tuesday (because the factory can work on at most five Product Xs at once), and hence at most 3 + 2 = 5 Product Xs could be assembled during the three days.
Therefore, the largest number of Product Xs that can be assembled during the three days is 5.
The correct answer is B.
We will determine the largest number of Product Xs that can be assembled during all three days by considering separately the largest number that can be assembled if 0, 1, 2, or 3 Product Xs begin assembly on Monday.
0 Product Xs begin assembly on Monday: In this case, at most three Product Xs can begin assembly on Tuesday (because only three units of Component A are available on Wednesday), and hence at most 0 + 3 = 3 Product Xs could be assembled during the three days.
1 Product X begins assembly on Monday: In this case, at most three Product Xs can begin assembly on Tuesday (because only three units of Component A are available on Wednesday), and hence at most 1 + 3 = 4 Product Xs could be assembled during the three days.
2 Product Xs begin assembly on Monday: In this case, at most three Product Xs can begin assembly on Tuesday (because only three units of Component A are available on Wednesday), and hence at most 2 + 3 = 5 Product Xs could be assembled during the three days.
3 Product Xs begin assembly on Monday: In this case, at most two Product Xs can begin assembly on Tuesday (because the factory can work on at most five Product Xs at once), and hence at most 3 + 2 = 5 Product Xs could be assembled during the three days.
Therefore, the largest number of Product Xs that can be assembled during the three days is 5.
The correct answer is B.
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