The maximum value of $Z=12 x+13 y$, subject to constraints $x \geq 0, y \geq 0, x+y \leq 5$ and $3 x+y \leq 9$ is

• A

  63
• Correct answer
  B

  65
• C

  60
• D

  117

Solution

Given constraints are $x \geq 0, y \geq 0, x+y \leq 5$ and $3 x+y \leq 9$ and $z=12 x+13 y$ The feasible region is $O A B C O$.
$\begin{aligned} & \because Z=12 x+13 y \\ & \text { At, } O(0,0), Z=12(0)+13(0)=0 \\ & \text { At, } A(3,0), Z=12(3)+13(0)=36 \\ & \text { At, } B(2,3), Z=12(2)+13(3)=63 \\ & \text { At, } C(0,5), Z=12(0)+13(5)=65 \end{aligned}$ Here, maximum value of $Z$ is 65 .

Hence, the correct answer is option: 'B'.