Question
Download Solution PDFCorner points of the feasible region for an LPP, are (0, 2), (3, 0), (6, 0) and (6, 8). If z = 2x + 3y is the objective function of LPP then max. (z)-min.(z) is equal to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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 z = 2x + 3y
Putting coordinates of points in the equation we get value of the point
e.g for corner point (0, 2)
z = 2x + 3y = 2 × 0 + 3 × 2 = 6
| Coordinate of point of corner points | value of Z |
| (0, 2) | 6 (min) |
| (3, 0) | 6 (min) |
| (6, 0) | 12 |
| (6, 8) | 36 (max) |
The difference of the maximum and minimum values of z is = 36 - 6 = 30
Last updated on Jul 4, 2025
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