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Home Questions TY5AWVX3M3
Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

Corner points of the feasible region for a linear programming problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0,5). Let F = 4x + 6y be the objective function. Then the minimum value of F occurs at :

Options:

(0, 2) only

(3, 0) only

The mid point of the line segment joining the points (0, 2) and (3, 0) only

Every point on the line segment joining the points (0, 2) and (3,0)

Correct Answer:

Every point on the line segment joining the points (0, 2) and (3,0)

Explanation:

Objective function F(x, y) = 4x + 6y

 Corner points   Value of F at points 
 (0, 2)   F(0, 2) = 0 + 6 × 2 = 12   Minimum value occurs at line joining two points on all points of line. 
 (3, 0)  F(3, 0) = 4 × 3 + 0 = 12 
 (6, 0)  F(6, 0) = 4 × 6 + 0 = 24  
 (6, 8)  F(6, 8) = 6 × 4 + 6 × 8 = 72   
 (0, 5)  F(0, 5) = 0 + 6 × 5 = 30  

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