The maximum value of $\mathrm{z}=3 x+5 y$ subject to the constraints $3 x+2 y \leq 18, x \leq 4, y \leq 6$,…

The maximum value of $\mathrm{z}=3 x+5 y$ subject to the constraints $3 x+2 y \leq 18, x \leq 4, y \leq 6$, $x, y \geq 0$, is
  1. $27$
  2. $36$
  3. $42$
  4. $30$

Solution

Objective function $\mathrm{z}=3 x+5 y$ The comer points of the feasible region are $\mathrm{O}(0,0), \mathrm{A}(4,0), \mathrm{B}(4,3), \mathrm{C}(2,6)$ and $\mathrm{D}(0,6)$ $\therefore \quad \mathrm{Z}$ at $\mathrm{A}(4,0)=12$ $\mathrm{Z}$ at $\mathrm{B}(4,3)=27$ $\mathrm{Z}$ at $\mathrm{C}(2,6)=36$ $\mathrm{Z}$ at $\mathrm{D}(0,6)=30$ $\therefore \quad$ Maximum value of $\mathrm{Z}$ is 36 .

Asked in: MHT CET 2023 (11 May Shift 2)

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