Question

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) only
2. (3, 0) only
3. 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 1

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 points	value 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)