If the corner points of the LPP, $$Z = 13x − 15y$$​ subject to the constraints $$x + y \le 7, 2x − 3y + 6 \ge 0, x \ge 0, y \ge 0$$​​
are (0,0), (7,0), (3,4) and (0,2), then the value of Maximum Z + 3 Minimum Z is:

Correct option is C

Given:
Z = 13x − 15y
Corner points:
(0,0), (7,0), (3,4), (0,2)
Formula used:
Maximum or minimum value of Z occurs at one of the corner points.
Solution:
Evaluate Z at each corner point:
At (0,0):
Z = 13(0) − 15(0) = 0
At (7,0):
Z = 13(7) − 15(0) = 91
At (3,4):
Z = 13(3) − 15(4) = 39 − 60 = −21
At (0,2):
Z = 13(0) − 15(2) = −30
Maximum Z = 91
Minimum Z = −30
Now,
Maximum Z + 3 Minimum Z
= 91 + 3(−30)
= 91 − 90
= 1
The correct answer is (c) 1.