A) \[max\text{ }Z=10~\]
B) \[max\text{ }Z=30\]
C) \[max\text{ }2=40\]
D) \[max\text{ }Z=50\]
E) None of these
Correct Answer: E
Solution :
We have, max \[Z=x+2y\] Subject to constraints, \[x-y\le 10\] \[2x+3y\le 20\] \[x\ge 0,\,\,y\ge 0\] On taking given constraints as equation, we get The following graph. Here, OAB is the required feasible region whose comer points are \[O(0,\,\,0),\,\,\,A(10,\,\,0)\] and \[B\left( 0,\frac{20}{3} \right)\].Comer point | \[z=x+2y\] |
at \[O(0,\,\,0)\] | \[Z=0\] |
at \[A\,(10,\,\,0)\] | \[Z=10\] |
at \[B\left( 0,\frac{20}{3} \right)\] | \[Z=0+2\times \frac{20}{3}=\frac{40}{3}\] |
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