1.

Let t = 2x + 3y be the objective function for all LPP and the corner points of the bounded feasible region are (6, 8), (6, 0), (0, 2), (0, 5). The minimum value of t occurs at:1. (0, 2) only2. (3, 0) only3. The midpoint of the line segment joining (0, 2) and (0, 3)4. Any point on the line segment joining (0, 2) and (0, 3)

Answer» Correct Answer - Option 1 : (0, 2) only

Concept:

Objective function: Linear function Z = ax + by, where a, b are constants, which has to be maximized or minimized is called a linear objective function.
In the above example, Z = ax + by is a linear objective function. Variables x and y are called decision variables.

By putting values of variables (coordinates of the point) in linear objective function we get the value of the point. 

Calculations:

Given:

Objective function for all LPP is t = 2x + 3y

Putting coordinates of points in the equation we gate value of the point

e.g for corner point (6, 8)

t = 2x + 3y = 2 × 6 + 3 × 8 = 36

Coordinate of point of corner pointsvalue of Z
(6, 8)36 (Max)
(6, 0)12
(0, 2)6 (Min)
(0, 3)9
(0, 5)15

Hence from the table, we can conclude that the minimum value of t occurs at (0, 2) 


Discussion

No Comment Found

Related InterviewSolutions