The maximum value of the objective function $\mathrm{z}=4 x+6 y$ subject to $3 x+2 y \leq 12, x+y \geq 4, x$, $y \geq 0$ is

• A

  24
• B

  46
• C

  56
• Correct answer
  D

  36

Solution

The corner points of feasible region are $\mathrm{A}(4,0)$, $\mathrm{B}(0,4), \mathrm{C}(0,6)$
At $A(4,0), Z=4(4)+6(0)=16$ At B( 0,4$), Z=4(0)+6(4)=24$ At $\mathrm{C}(0,6), \mathrm{Z}=4(0)+6(6)=36$ $\therefore \quad \mathrm{Z}$ has maximum value at $\mathrm{C}(0,6)$ which is 36 .

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