The maximum value of the objective function $\mathrm{z}=2 \mathrm{x}+3 \mathrm{y}$ subject to the…

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
  1. 15
  2. 10
  3. 20
  4. 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 $\begin{aligned} \mathrm{Z}=2 \mathrm{x} & +3 \mathrm{y} \\ \therefore \quad \mathrm{z}_{\mathrm{A}} & =2(0)+3(4)=12 \\ \mathrm{Z}_{\mathrm{B}} & =2(2)+3(0)=4 \\ \mathrm{Z}_{\mathrm{C}} & =2(5)+3(0)=10 \\ \mathrm{Z}_{\mathrm{D}} & =2(0)+3(5)=15 \end{aligned}$

Asked in: MHT CET 2021 (23 Sep Shift 2)

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