The maximum value of the objective function $\mathrm{z}=2 \mathrm{x}+3 \mathrm{y}$ subject to the constraints $\mathrm{x}+\mathrm{y} \leq 5,2 \mathrm{x}+\mathrm{y} \geq 4$ and $\mathrm{x} \geq 0, \mathrm{y} \geq 0$ is

• Correct answer
  A

  15
• B

  10
• C

  20
• D

  25

Solution

Refer Figure
Required part is shaded. We have $\mathrm{A}=(0,4)$; $$ \begin{aligned} & \mathrm{B}=(2,0) ; \mathrm{C}=(5,0) \\ & \mathrm{D}=(0,5) \end{aligned} $$ We have to maximize function $$ \begin{aligned} \mathrm{Z}=2 \mathrm{x} & +3 \mathrm{y} \\ \therefore \quad \mathrm{z}_{\mathrm{A}} & =2(0)+3(4)=12 \\ \mathrm{Z}_{\mathrm{B}} & =2(2)+3(0)=4 \\ \mathrm{Z}_{\mathrm{C}} & =2(5)+3(0)=10 \\ \mathrm{Z}_{\mathrm{D}} & =2(0)+3(5)=15 \end{aligned} $$

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