A) \[20\,at\,(1,0)\]
B) \[30\,\,at\,\,(0,6)\]
C) \[37\,at\,(4,5)\]
D) \[33\,\,at\,\,(6,3)\]
Correct Answer: C
Solution :
| [c] We have, maximize \[Z=3x+5y\]subject to constraints:\[x+4y\le 24,3x+y\le 21,x+y\le 9,x\ge 0,y\ge 0\] |
| Let \[{{\ell }_{1}}:x+4y=24\] |
| \[{{\ell }_{2}}:3x+y=21\] |
| \[{{\ell }_{3}}:x+y=9\] |
| \[{{\ell }_{4}}:x=0\] and \[{{\ell }_{5}}:y=0\] |
| On solving these equations we will get points as |
| O (0, 0), A (7, 0), B (6, 3), C (4, 5), D (0, 6) |
| Now maximize \[Z=3x+5y\] |
| \[ZatO(0,0)=3(0)+5(0)=0\] |
| \[ZatA(7,0)=3(7)+5(0)=21\] |
| \[ZatB(6,3)=3(6)+5(3)=33\] |
| \[ZatC(4,5)=3(4)+5(5)=37\] |
| \[ZatD(0,6)=3(0)+5(6)=30\] |
| Thus, Z is maximized at C (4, 5) and its maximum value is 37. |
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