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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.

Each line must receive more than half its maximum and must be an integer.

So, A must receive, 42/2+1=22

Now, we are left with, 45-22=23 hours.
C must receive, 12/2+1=7, then B can receive 23-7=16.

Answer: B=16, C=7.
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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 B Line C
6
7
8
16
17


Greater than 1/2 of 42 is >21
Greater than 1/2 of 20 is >10
Greater than 1/2 of 12 is >6

Thus total is 22+11+7=40 and we need 5 more hours so using the answer choices 22, 16, 7 is a possible combination

Ans 16,7
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Line A must have at least 22 hours, Line B must have at least 11 hours and Line C must have at least 7 hours. Total: 40 hours.

As 45 hours must be used, we have 5 additional hours that must be distrubuted among the three lines.

With trial and error, the correct answer is Line B=16 and Line C=7.
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The conditions means that Line must have at least 22, Line B at least 11 and Line C at least 7

Given the choices B can either be 16 or 17 while C can only be 7 or 8
Testing each case only 16+7 = 23 leaves a figure greater than 21 (45-23=22) Hence B is 16 and C is 7
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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.
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we need A+B+C=45,
such that A>21,B>10 and C> 6
let's use the options so put different values,

A B C = A+B+C
23 17 7 = 47
23 16 7 = 46
22 17 7 =46
22 16 7= 45

so B=16 and C= 7 should be the ans.
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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.
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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 BLine C
6
7
8
16
17


Given that, 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.

So, for Line A = 21 < a <= 42................(1)
for Line B = 10 < a <= 20.................(2)
for Line C = 6 < a <= 12...................(3)

Putting Line C = 6 ( NOT possible...as per constraint (3) )
Putting Line C = 7, Line B = 16, Line A = 22 (all constraints satisfied)
Putting Line C = 7, Line B = 17, Line A = 21 ( NOT possible...as per constraint (1) )
Putting Line C = 8, Line B = 16, Line A = 21 ( NOT possible...as per constraint (1) )

thus, only Line B = 16; Line C = 7 satisfies all the constraints



Line B = 16
Line C = 7 is the CORRECT answer
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Solution Explanation:
We need to allocate 45 hours among three production lines (A, B, and C) with the following constraints:
  1. Line A:
    • Minimum: More than half of 42 → >21 hours
    • Maximum: 42 hours
  2. Line B:
    • Minimum: More than half of 20 → >10 hours
    • Maximum: 20 hours
  3. Line C:
    • Minimum: More than half of 12 → >6 hours
    • Maximum: 12 hours
All allocations must be integers, and the total must add up to 45 hours.
Step-by-Step Allocation:
  1. Possible Hours for Each Line:
    • Line A: 22 to 42 hours
    • Line B: 11 to 20 hours
    • Line C: 7 to 12 hours
  2. Given Options:
    • Line B: 6, 7, 8, 16, 17
    • Line C: 6, 7, 8, 16, 17
  3. Determine Valid Selections:
    • For Line B:
      • Valid Options (must be >10): 16, 17
    • For Line C:
      • Valid Options (must be >6 and ≤12): 7, 8
  4. Check Combinations:
    • Option 1:
      • Line B = 16
      • Line C = 7
      • Line A = 45 - 16 - 7 = 22 (Valid, since >21)
    • Option 2:
      • Line B = 16
      • Line C = 8
      • Line A = 45 - 16 - 8 = 21 (Invalid, since ≤21)
    • Option 3:
      • Line B = 17
      • Line C = 7
      • Line A = 45 - 17 - 7 = 21 (Invalid, since ≤21)
    • Option 4:
      • Line B = 17
      • Line C = 8
      • Line A = 45 - 17 - 8 = 20 (Invalid, since <21)
  5. Valid Combination:
    • Line B = 16 hours
    • Line C = 7 hours
    • Line A = 22 hours
Final Answer:
Line BLine C
167
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From the task, we get:
  • \(21<a<=42\)
  • \(10<b<=20\)
  • \(6<c<=12\)

Then, the minimal value for A is 22; for B it's 11 and for C it's 7.

From the suggested answers, B can be only 16 and 17.
  • Checking 16, we get \(a+c=45-16=29\), and with the minimal value for c=7 we also get a=22; this is consistent.
  • Checking 17, we get \(a+c= 45-17=28\), and with the minimal value for c=7 we also get a=21; this is inconsistent as A must be above 21.

The answer is b=16 and c=7.
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Distribute 45 hrs among A, B, C

More than half max for each line

A > 21
B > 10
C > 6

Question : Possible B ? C?

In given options possible B = 16, 17

In given options possible C = 7, 8, 16, 17

Assume A has lowest possible = 22

Remaining = 23hrs

B has atleast 11 and C has atleast 7, remaining 5 hrs can be distributed between B and C

Maximum B can have = 11 + 5 = 16

(B, C) = (16, 7)



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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.
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A>21
B>10
C>6

Therefore keeping A min = 22 based on options keeping C min at 7 and checking if B works. B 17 works when C @ 7 imo this is the answer
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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.
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Total Hours A+B+C = 45
Max(A) = 42 Min(A) = 42/2 = 21
Max(B) = 20 Min(B) = 20/2 = 10
Max(C) = 12 Min(C) = 12/2 = 6

Now, we know that min should be more than half of maximum,
So,
22<= A <=42
11<= B <=20
7<= C <=12

These are the possible valid ranges
Now,
A = 45 - B - C and should satisfy above ranges
Lets substitute value 1 by 1
B = 16, C=7
A = 45 -16-7 = 22 (This is valid)

Since we see this to be valid, we can assume the rest as invalid
So,
B = 16
C = 7
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line a - must be b/w 22 and 42
line b - must be b/w 11 and 20
line c - must be between 11 and 12

hours(a) + hours(b) + hours(c) = 45

testing possible values of a,b,and c
(I)
b=17,c=8
a = 20
Not valid

(II)
b=16, c=8
a = 21
valid

Answer -
line b = 16
line c = 8
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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.
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IMO

Line B: 16 hours
Line C: 7 hours



Lets analyze the
Constraints:
  • Line A: Maximum 42 hours, must receive more than half its maximum (more than 21 hours).
  • Line B: Maximum 20 hours, must receive more than half its maximum (more than 10 hours).
  • Line C: Maximum 12 hours, must receive more than half its maximum (more than 6 hours).
  • Total hours to be distributed: 45 hours.


Now for B the only possibility from the option is

either 16 or 17

if we take 16 then

B= 16
A>= 22( can't be 21)

then c is 7 which is the answer because of the constraint c can be less than 7
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Line A: Maximum 42 hours, Minimum: 42 / 2 = 21 hours
line B: Maximum 20 hours, Minimum: 20 / 2 = 10 hours
line C: Maximum 12 hours, Minimum: 12 / 2 = 6 hours

Line B
Possible values: 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
Line C
Possible values: 7, 8, 9, 10, 11, 12

Trial and error with the possibilities
we get b = 16 and c = 8



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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.
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Eliminate answer "6" as:
LINE A > 21
LINE B > 10
LINE C > 6

A+B+C = 45
A<= 42; B<= 20; C<= 12

Trying values starting with the most limited option, C then prove with the rest of variables.

C = 7 then A+B = 38 and given A must be at least 22, 38-22= 16 which is an available option for B.

C=7
B=16
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Given lower limits of half their maximum and their maximum values I'd try plugging in the answers given restrictions.

Do not try 6 as an option, since it does not comply with the restriction on C so

A+B+C = 45

C = 7 then A+B = 45 - 7= 38

A must be more than 21, let's try with 22 so B = 38-22= 16

B =16 and C = 7
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