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24 Jan 2025, 09:43
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Line B: 16
Line C: 7
A plant must distribute 45 hours weekly among three production lines: A, B, and C.
• Line A: Maximum 42 hours
• Line B: Maximum 20 hours
• Line C: Maximum 12 hours
Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.
Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
• Line A: Maximum 42 hours
• Line B: Maximum 20 hours
• Line C: Maximum 12 hours
Each line must receive more than half its maximum, all 45 hours must be used, and the number of hours allocated to each line must be an integer.
Select for Line B the hours that could have been allocated to Line B, and select for Line C the hours that could have been allocated to Line C that would be jointly consistent with the given information. Make only two selections, one in each column.
| Line B | Line C | |
| 6 | ||
| 7 | ||
| 8 | ||
| 16 | ||
| 17 |
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Official Answer
Line B: 16
Line C: 7
24 Jan 2025, 09:43
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Official Solution:
Since each line must receive more than half its maximum:
• A got at least 42/2 + 1 = 22 hours, leaving for B and C at most 45 - 22 = 23 hours.
• B must receive at least 20/2 + 1 = 11 hours.
• C must receive at least 12/2 + 1 = 7 hours.
Thus:
11 ≤ B ≤ 20
7 ≤ C ≤ 12
From the total allocation:
18 ≤ B + C ≤ 23
From the options, only B = 16 and C = 7 satisfy these conditions.
Correct answer:
Line B "16"
Line C "7"
Bunuel
Since each line must receive more than half its maximum:
• A got at least 42/2 + 1 = 22 hours, leaving for B and C at most 45 - 22 = 23 hours.
• B must receive at least 20/2 + 1 = 11 hours.
• C must receive at least 12/2 + 1 = 7 hours.
Thus:
11 ≤ B ≤ 20
7 ≤ C ≤ 12
From the total allocation:
18 ≤ B + C ≤ 23
From the options, only B = 16 and C = 7 satisfy these conditions.
Correct answer:
Line B "16"
Line C "7"
