Question

Match LIST I with LIST II

List-I		List-II
A	If the corner points of the feasible region For an LPP are (0, 4), (5, 0), (7, 9), then the minimum value of the objective function Z =5x+y is.	I	27
B	If the corner points of the feasible region for an LPP are (0, 0), (0, 2), (3, 4), (5, 3). then the maximum value of the objective function Z=3x+4y	II	60
C	The comer points of the feasible region for an LPP are (0, 2), (1, 2), (4,3), (7, 0). The objective function is Z = x+5y. Then (Max Z+Min Z) is	III	25
D	If the corner points of the feasible region for an LPP are (0, 4), (3, 0), (3, 2), (6,9) The objective function is Z=2x+6y. Then (Max Z-Min Z)	IV	26

Choose the correct answer from the options given below

• A. A-III, B-IV, C-I, D-II
• B. A-III, B-I, C-IV, D-II
• C. A-IV,B-III,C-II, D-I
• D. A-I, B-III, C-IV, D-II

Answer 1

The Correct Option is B

To solve the problem, calculate the objective function value for each corner point of the feasible region, then determine the minimum or maximum value as required. Let's examine each case:

1. Case A: Corner points: (0, 4), (5, 0), (7, 9). Objective Function: Z = 5x + y.
   • For (0, 4): Z=5(0)+4=4
   • For (5, 0): Z=5(5)+0=25
   • For (7, 9): Z=5(7)+9=44
   Minimum Z is 4, which does not match List-II. Incorrect match.
2. Case B: Corner points: (0, 0), (0, 2), (3, 4), (5, 3). Objective Function: Z = 3x + 4y.
   • For (0, 0): Z=3(0)+4(0)=0
   • For (0, 2): Z=3(0)+4(2)=8
   • For (3, 4): Z=3(3)+4(4)=25
   • For (5, 3): Z=3(5)+4(3)=29
   Maximum Z is 29, which matches I. The correct match is B-I.
3. Case C: Corner points: (0, 2), (1, 2), (4, 3), (7, 0). Objective Function: Z = x + 5y.
   • For (0, 2): Z=0+5(2)=10
   • For (1, 2): Z=1+5(2)=11
   • For (4, 3): Z=4+5(3)=19
   • For (7, 0): Z=7+5(0)=7
   Max Z is 19, Min Z is 7. Sum = 26, which matches IV. The correct match is C-IV.
4. Case D: Corner points: (0, 4), (3, 0), (3, 2), (6, 9). Objective Function: Z = 2x + 6y.
   • For (0, 4): Z=2(0)+6(4)=24
   • For (3, 0): Z=2(3)+6(0)=6
   • For (3, 2): Z=2(3)+6(2)=18
   • For (6, 9): Z=2(6)+6(9)=66
   Max Z is 66, Min Z is 6. Difference = 60, which matches II. Correct match is D-II.

Therefore, the correct option is:

A-III, B-I, C-IV, D-II