A) Exactly one pint
B) Exactly two points
C) Infinitely many points
D) None of these
Correct Answer: C
Solution :
[c] We find that the feasible region is on the same side of the line \[2x+5y=10\]as the origin, on the same side of the line \[x-y=4\]as the origin and on the opposite side of the line \[x+2y=1\]from the origin. Moreover, the lines meet the coordinate axes at (5, 0), (0, 2); (1, 0), (0, 1/2) and (4, 0). The lines \[x-=4\]and \[2x+5y=10\]intersect at\[\left( \frac{30}{7},\frac{2}{7} \right)\] |
The values of the objective function at the vertices of the pentagon are: |
(i) \[Z=0+\frac{5}{2}=\frac{5}{2a}\] |
(ii) \[Z=2+0=2\] |
(iii) \[Z=8+0=8\] |
(iv) \[Z=\frac{60}{7}+\frac{10}{7}=10\] |
(v) \[Z=0+10=10\] |
The maximum value 10 occurs at the points D (30/7, 2/7) and E (0, 2). Since D and E are adjacent vertices, the objective function has the same maximum value 10 at all the points on the lines DE. |
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